#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/STACK:36777216")
template <class T>
inline T &RD(T &);
template <class T>
inline void OT(const T &);
inline long long RD() {
  long long x;
  return RD(x);
}
inline char &RC(char &c) {
  scanf(" %c", &c);
  return c;
}
inline char RC() {
  char c;
  return RC(c);
}
inline double &RF(double &x) {
  scanf("%lf", &x);
  return x;
}
inline double RF() {
  double x;
  return RF(x);
}
inline char *RS(char *s) {
  scanf("%s", s);
  return s;
}
template <class T0, class T1>
inline T0 &RD(T0 &x0, T1 &x1) {
  RD(x0), RD(x1);
  return x0;
}
template <class T0, class T1, class T2>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2) {
  RD(x0), RD(x1), RD(x2);
  return x0;
}
template <class T0, class T1, class T2, class T3>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  RD(x0), RD(x1), RD(x2), RD(x3);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);
  return x0;
}
template <class T0, class T1>
inline void OT(const T0 &x0, const T1 &x1) {
  OT(x0), OT(x1);
}
template <class T0, class T1, class T2>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2) {
  OT(x0), OT(x1), OT(x2);
}
template <class T0, class T1, class T2, class T3>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3) {
  OT(x0), OT(x1), OT(x2), OT(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5, const T6 &x6) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);
}
inline char &RC(char &a, char &b) {
  RC(a), RC(b);
  return a;
}
inline char &RC(char &a, char &b, char &c) {
  RC(a), RC(b), RC(c);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d) {
  RC(a), RC(b), RC(c), RC(d);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e) {
  RC(a), RC(b), RC(c), RC(d), RC(e);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g);
  return a;
}
inline double &RF(double &a, double &b) {
  RF(a), RF(b);
  return a;
}
inline double &RF(double &a, double &b, double &c) {
  RF(a), RF(b), RF(c);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d) {
  RF(a), RF(b), RF(c), RF(d);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e) {
  RF(a), RF(b), RF(c), RF(d), RF(e);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f, double &g) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g);
  return a;
}
inline void RS(char *s1, char *s2) { RS(s1), RS(s2); }
inline void RS(char *s1, char *s2, char *s3) { RS(s1), RS(s2), RS(s3); }
template <class T>
inline void RST(T &A) {
  memset(A, 0, sizeof(A));
}
template <class T0, class T1>
inline void RST(T0 &A0, T1 &A1) {
  RST(A0), RST(A1);
}
template <class T0, class T1, class T2>
inline void RST(T0 &A0, T1 &A1, T2 &A2) {
  RST(A0), RST(A1), RST(A2);
}
template <class T0, class T1, class T2, class T3>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  RST(A0), RST(A1), RST(A2), RST(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);
}
template <class T>
inline void FLC(T &A, int x) {
  memset(A, x, sizeof(A));
}
template <class T0, class T1>
inline void FLC(T0 &A0, T1 &A1, int x) {
  FLC(A0, x), FLC(A1, x);
}
template <class T0, class T1, class T2>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x);
}
template <class T0, class T1, class T2, class T3>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x),
      FLC(A6, x);
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, less<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(T &A) {
  A.clear();
}
template <class T0, class T1>
inline void CLR(T0 &A0, T1 &A1) {
  CLR(A0), CLR(A1);
}
template <class T0, class T1, class T2>
inline void CLR(T0 &A0, T1 &A1, T2 &A2) {
  CLR(A0), CLR(A1), CLR(A2);
}
template <class T0, class T1, class T2, class T3>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);
}
template <class T>
inline void CLR(T &A, int n) {
  for (int i = 0; i < int(n); ++i) CLR(A[i]);
}
template <class T>
inline T &SRT(T &A) {
  sort(A.begin(), A.end());
  return A;
}
template <class T, class C>
inline T &SRT(T &A, C B) {
  sort(A.begin(), A.end(), B);
  return A;
}
const int dx4[] = {-1, 0, 1, 0};
const int dy4[] = {0, 1, 0, -1};
const int dx8[] = {-1, 0, 1, 0, -1, -1, 1, 1};
const int dy8[] = {0, 1, 0, -1, -1, 1, -1, 1};
const int dxhorse[] = {-2, -2, -1, -1, 1, 1, 2, 2};
const int dyhorse[] = {1, -1, 2, -2, 2, -2, 1, -1};
const int MOD = 1e9 + 9;
const int INF = 0x3f3f3f3f;
const long long INFF = 1LL << 60;
const double EPS = 1e-9;
const double OO = 1e15;
const double PI = acos(-1.0);
template <class T>
inline void checkMin(T &a, const T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkMax(T &a, const T b) {
  if (a < b) a = b;
}
template <class T>
inline void checkMin(T &a, T &b, const T x) {
  checkMin(a, x), checkMin(b, x);
}
template <class T>
inline void checkMax(T &a, T &b, const T x) {
  checkMax(a, x), checkMax(b, x);
}
template <class T, class C>
inline void checkMin(T &a, const T b, C c) {
  if (c(b, a)) a = b;
}
template <class T, class C>
inline void checkMax(T &a, const T b, C c) {
  if (c(a, b)) a = b;
}
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline T sqr(T a) {
  return a * a;
}
template <class T>
inline T cub(T a) {
  return a * a * a;
}
inline int Ceil(int x, int y) { return (x - 1) / y + 1; }
namespace BO {
inline bool _1(int x, int i) { return bool(x & 1 << i); }
inline bool _1(long long x, int i) { return bool(x & 1LL << i); }
inline long long _1(int i) { return 1LL << i; }
inline long long _U(int i) { return _1(i) - 1; };
inline int reverse_bits(int x) {
  x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
  x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
  x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
  x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
  x = ((x >> 16) & 0x0000ffff) | ((x << 16) & 0xffff0000);
  return x;
}
inline long long reverse_bits(long long x) {
  x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
  x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
  x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
  x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
  x = ((x >> 16) & 0x0000ffff0000ffffLL) | ((x << 16) & 0xffff0000ffff0000LL);
  x = ((x >> 32) & 0x00000000ffffffffLL) | ((x << 32) & 0xffffffff00000000LL);
  return x;
}
template <class T>
inline bool odd(T x) {
  return x & 1;
}
template <class T>
inline T low_bit(T x) {
  return x & -x;
}
template <class T>
inline T high_bit(T x) {
  T p = low_bit(x);
  while (p != x) x -= p, p = low_bit(x);
  return p;
}
template <class T>
inline T cover_bit(T x) {
  T p = 1;
  while (p < x) p <<= 1;
  return p;
}
inline int low_idx(int x) { return __builtin_ffs(x); }
inline int low_idx(long long x) { return __builtin_ffsll(x); }
inline int high_idx(int x) { return low_idx(reverse_bits(x)); }
inline int high_idx(long long x) { return low_idx(reverse_bits(x)); }
inline int clz(int x) { return __builtin_clz(x); }
inline int clz(long long x) { return __builtin_clzll(x); }
inline int ctz(int x) { return __builtin_ctz(x); }
inline int ctz(long long x) { return __builtin_ctzll(x); }
inline int parity(int x) { return __builtin_parity(x); }
inline int parity(long long x) { return __builtin_parityll(x); }
inline int lg2(int a) { return 31 - __builtin_clz(a); }
inline int count_bits(int x) { return __builtin_popcount(x); }
inline int count_bits(long long x) { return __builtin_popcountll(x); }
}  // namespace BO
using namespace BO;
namespace NT {
inline void INC(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
}
inline int sum(int a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
  return a;
}
inline void DEC(int &a, int b) {
  a -= b;
  if (a < 0) a += MOD;
}
inline int dff(int a, int b) {
  a -= b;
  if (a < 0) a += MOD;
  return a;
}
inline void MUL(int &a, int b) { a = (long long)a * b % MOD; }
inline int pdt(int a, int b) { return (long long)a * b % MOD; }
inline int sum(int a, int b, int c) { return sum(sum(a, b), c); }
inline int sum(int a, int b, int c, int d) { return sum(sum(a, b), sum(c, d)); }
inline int pdt(int a, int b, int c) { return pdt(pdt(a, b), c); }
inline int pdt(int a, int b, int c, int d) { return pdt(pdt(pdt(a, b), c), d); }
inline int pow(int a, long long b) {
  int c(1);
  while (b) {
    if (b & 1) MUL(c, a);
    MUL(a, a), b >>= 1;
  }
  return c;
}
template <class T>
inline T pow(T a, long long b) {
  T c(1);
  while (b) {
    if (b & 1) c *= a;
    a *= a, b >>= 1;
  }
  return c;
}
inline int _I(int b) {
  int a = MOD, x1 = 0, x2 = 1, q;
  while (true) {
    q = a / b, a %= b;
    if (!a) return (x2 + MOD) % MOD;
    DEC(x1, pdt(q, x2));
    q = b / a, b %= a;
    if (!b) return (x1 + MOD) % MOD;
    DEC(x2, pdt(q, x1));
  }
}
inline void DIA(int &a, int b) { MUL(a, _I(b)); }
inline int qtt(int a, int b) { return pdt(a, _I(b)); }
inline int phi(int n) {
  int res = n;
  for (int i = 2; sqr(i) <= n; ++i)
    if (!(n % i)) {
      DEC(res, qtt(res, i));
      do {
        n /= i;
      } while (!(n % i));
    }
  if (n != 1) DEC(res, qtt(res, n));
  return res;
}
template <class T>
T GCD(T a, T b) {
  return b ? GCD(b, a % b) : a;
}
template <class T>
T extendGCD(T a, T b, T &x, T &y) {
  if (!b) return x = 1, y = 0, a;
  T res = extendGCD(b, a % b, x, y), tmp = x;
  x = y, y = tmp - (a / b) * y;
  return res;
}
template <class T>
inline T inv(T w, T M) {
  if (M <= 0) return -1;
  T x, y, d;
  d = extendGCD(w, M, x, y);
  if (d != 1) return -1;
  x = ((x % M) + M) % M;
  return x;
}
}  // namespace NT
using namespace NT;
namespace RNG {
inline unsigned int rand16() { return (bool(rand() & 1) << 15) | rand(); }
inline unsigned int rand32() { return (rand16() << 16) | rand16(); }
inline unsigned long long rand64() {
  return ((long long)rand32() << 32) | rand32();
}
inline unsigned long long random(long long l, long long r) {
  return rand64() % (r - l) + l;
}
int dice() { return rand() % 6; }
bool coin() { return bool(rand() % 2); }
};  // namespace RNG
namespace CLOCK {
double s0, s1, rd, k, T;
inline double getTime() { return 1.0 * clock() / CLOCKS_PER_SEC; }
inline void st0(double _T = 0.98) { T = _T, s0 = getTime(); }
inline void st1(double _k = 1.618) { k = _k, s1 = getTime(); }
inline void ed1() { rd = getTime() - s1; }
inline double elapsed() { return getTime() - s0; }
inline bool safe() { return elapsed() + rd * k < T; }
}  // namespace CLOCK
template <class T>
pair<T, T> operator+(const pair<T, T> &p1, const pair<T, T> &p2) {
  return pair<T, T>(p1.first + p2.first, p1.second + p2.second);
}
template <class T>
pair<T, T> operator-(const pair<T, T> &p1, const pair<T, T> &p2) {
  return pair<T, T>(p1.first - p2.first, p1.second - p2.second);
}
template <class T>
pair<T, T> operator*(const pair<T, T> &lhs, T k) {
  return pair<T, T>(lhs.first * k, lhs.second * k);
}
namespace Math {
long long GCD(long long a, long long b) { return b ? GCD(b, a % b) : a; }
long long extendGCD(long long a, long long b, long long &x, long long &y) {
  if (!b) return x = 1, y = 0, a;
  long long res = extendGCD(b, a % b, x, y), tmp = x;
  x = y, y = tmp - (a / b) * y;
  return res;
}
long long power(long long x, long long k) {
  long long res = 1;
  while (k) {
    if (k & 1) res *= x;
    x *= x, k >>= 1;
  }
  return res;
}
long long powerMod(long long x, long long k, long long m) {
  long long res = 1;
  while (x %= m, k) {
    if (k & 1) res *= x, res %= m;
    x *= x, k >>= 1;
  }
  return res;
}
long long inverse(long long a, long long p, long long t = 1) {
  long long pt = power(p, t);
  long long x, y;
  y = extendGCD(a, pt, x, y);
  return x < 0 ? x += pt : x;
}
long long linearCongruence(long long a, long long b, long long p, long long q) {
  long long x, y;
  y = extendGCD(p, q, x, y);
  while (b < a) b += q / y;
  x *= b - a, x = p * x + a, x %= p * q;
  if (x < 0) x += p * q;
  return x;
}
const int PRIMERANGE = 1000000;
int prime[PRIMERANGE + 1];
int getPrime() {
  memset(prime, 0, sizeof(int) * (PRIMERANGE + 1));
  for (int i = 2; i <= PRIMERANGE; i++) {
    if (!prime[i]) prime[++prime[0]] = i;
    for (int j = 1; j <= prime[0] && prime[j] <= PRIMERANGE / i; j++) {
      prime[prime[j] * i] = 1;
      if (i % prime[j] == 0) break;
    }
  }
  return prime[0];
}
int factor[100][3], facCnt;
int getFactors(int x) {
  facCnt = 0;
  int tmp = x;
  for (int i = 1; prime[i] <= tmp / prime[i]; i++) {
    factor[facCnt][1] = 1, factor[facCnt][2] = 0;
    if (tmp % prime[i] == 0) factor[facCnt][0] = prime[i];
    while (tmp % prime[i] == 0)
      factor[facCnt][2]++, factor[facCnt][1] *= prime[i], tmp /= prime[i];
    if (factor[facCnt][1] > 1) facCnt++;
  }
  if (tmp != 1)
    factor[facCnt][0] = tmp, factor[facCnt][1] = tmp, factor[facCnt++][2] = 1;
  return facCnt;
}
long long combinationModP(long long n, long long k, long long p) {
  if (k > n) return 0;
  if (n - k < k) k = n - k;
  long long a = 1, b = 1, x, y;
  int pcnt = 0;
  for (int i = 1; i <= k; i++) {
    x = n - i + 1, y = i;
    while (x % p == 0) x /= p, pcnt++;
    while (y % p == 0) y /= p, pcnt--;
    x %= p, y %= p, a *= x, b *= y;
    b %= p, a %= p;
  }
  if (pcnt) return 0;
  extendGCD(b, p, x, y);
  if (x < 0) x += p;
  a *= x, a %= p;
  return a;
}
};  // namespace Math
namespace Geo {
const int eps = 1e-8;
int dblcmp(double d) {
  if (fabs(d) < eps) return 0;
  return d > eps ? 1 : -1;
}
int sgn(double a) { return a < -eps ? -1 : a > eps; }
inline double sqr(double x) { return x * x; }
struct Point2D {
  int x, y;
  Point2D() {}
  Point2D(int _x, int _y) : x(_x), y(_y){};
  void input() { scanf("%d%d", &x, &y); }
  void output() { printf("%.2f %.2f\n", x, y); }
  bool operator==(Point2D a) const {
    return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0;
  }
  bool operator<(Point2D a) const {
    return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;
  }
  int len() { return hypot(x, y); }
  int len2() { return x * x + y * y; }
  Point2D operator+(const Point2D &A) const {
    return Point2D(x + A.x, y + A.y);
  }
  Point2D operator-(const Point2D &A) const {
    return Point2D(x - A.x, y - A.y);
  }
  Point2D operator*(const int _x) const { return Point2D(x * _x, y * _x); }
  int operator*(const Point2D &A) const { return x * A.x + y * A.y; }
  int operator^(const Point2D &A) const { return x * A.y - y * A.x; }
  Point2D operator/(const int _p) const { return Point2D(x / _p, y / _p); }
  int distance(Point2D p) { return hypot(x - p.x, y - p.y); }
  Point2D add(Point2D p) { return Point2D(x + p.x, y + p.y); }
  Point2D sub(Point2D p) { return Point2D(x - p.x, y - p.y); }
  Point2D mul(int b) { return Point2D(x * b, y * b); }
  Point2D div(int b) { return Point2D(x / b, y / b); }
  int dot(Point2D p) { return x * p.x + y * p.y; }
  int det(Point2D p) { return x * p.y - y * p.x; }
  int rad(Point2D a, Point2D b) {
    Point2D p = *this;
    return fabs(atan2(fabs(a.sub(p).det(b.sub(p))), a.sub(p).dot(b.sub(p))));
  }
  Point2D trunc(int r) {
    int l = len();
    if (!dblcmp(l)) return *this;
    r /= l;
    return Point2D(x * r, y * r);
  }
  Point2D rotleft() { return Point2D(-y, x); }
  Point2D rotright() { return Point2D(y, -x); }
  Point2D rotate(Point2D p, int angle) {
    Point2D v = this->sub(p);
    int c = cos(angle), s = sin(angle);
    return Point2D(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
int cross(Point2D a, Point2D b, Point2D c) { return (b.sub(a)).det(c.sub(a)); }
}  // namespace Geo
using namespace Geo;
template <class T>
inline T &RD(T &ret) {
  char c;
  int sgn;
  c = getchar();
  while (c != '-' && (c < '0' || c > '9')) c = getchar();
  sgn = (c == '-') ? -1 : 1;
  ret = (c == '-') ? 0 : (c - '0');
  while (c = getchar(), c >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  ret *= sgn;
  return ret;
}
int ____Case;
template <class T>
inline void OT(const T &x) {
  printf("%d\n", x);
}
int dp[2][33][33][33][2];
int n, m;
void solve() {
  RST(dp);
  dp[1][0][0][0][1] = 4;
  int now = 1, nex = 0;
  for (int i = 1; i < n; ++i, swap(now, nex)) {
    RST(dp[nex]);
    for (int j = 0; j < int(m); ++j)
      for (int p = 0; p < int(m); ++p)
        for (int q = 0; q < int(m); ++q)
          for (int ok = 0; ok < int(2); ++ok) {
            INC(dp[nex][((j ? (j + 1) % m : 0))][((p ? (p + 1) % m : 0))]
                  [((q ? (q + 1) % m : 0))][(ok)],
                dp[now][j][p][q][ok]);
            INC(dp[nex][(ok)][((p ? (p + 1) % m : 0))][((q ? (q + 1) % m : 0))]
                  [(i < m || j)],
                dp[now][j][p][q][ok]);
            INC(dp[nex][((j ? (j + 1) % m : 0))][(ok)][((q ? (q + 1) % m : 0))]
                  [(i < m || p)],
                dp[now][j][p][q][ok]);
            INC(dp[nex][((j ? (j + 1) % m : 0))][((p ? (p + 1) % m : 0))][(ok)]
                  [(i < m || q)],
                dp[now][j][p][q][ok]);
          }
  }
  int ans = 0;
  for (int j = 0; j < int(m); ++j)
    for (int p = 0; p < int(m); ++p)
      for (int q = 0; q < int(m); ++q) {
        INC(ans, dp[n & 1][j][p][q][1]);
        if (j + p + q) INC(ans, dp[n & 1][j][p][q][0]);
      }
  OT(ans);
}
int main() {
  while (cin >> n >> m) solve();
}
