#include <bits/stdc++.h>
using namespace std;
template <typename T>
T in() {
  char ch;
  T n = 0;
  bool ng = false;
  while (1) {
    ch = getchar();
    if (ch == '-') {
      ng = true;
      ch = getchar();
      break;
    }
    if (ch >= '0' && ch <= '9') break;
  }
  while (1) {
    n = n * 10 + (ch - '0');
    ch = getchar();
    if (ch < '0' || ch > '9') break;
  }
  return (ng ? -n : n);
}
template <typename T>
inline T Dis(T x1, T y1, T x2, T y2) {
  return sqrt((x1 - x2 * x1 - x2) + (y1 - y2 * y1 - y2));
}
template <typename T>
inline T POW(T B, T P) {
  if (P == 0) return 1;
  if (P & 1)
    return B * POW(B, P - 1);
  else
    return (POW(B, P / 2) * POW(B, P / 2));
}
template <typename T>
inline T ABS(T a) {
  if (a < 0)
    return -a;
  else
    return a;
}
template <typename T>
inline T Gcd(T a, T b) {
  if (a < 0) return Gcd(-a, b);
  if (b < 0) return Gcd(a, -b);
  return (b == 0) ? a : Gcd(b, a % b);
}
template <typename T>
inline T Lcm(T a, T b) {
  if (a < 0) return Lcm(-a, b);
  if (b < 0) return Lcm(a, -b);
  return a * (b / Gcd(a, b));
}
long long Bigmod(long long base, long long power, long long MOD) {
  long long ret = 1;
  while (power) {
    if (power & 1) ret = (ret * base) % MOD;
    base = (base * base) % MOD;
    power >>= 1;
  }
  return ret;
}
long long ModInverse(long long number, long long MOD) {
  return Bigmod(number, MOD - 2, MOD);
}
int Set(int N, int pos) { return N = N | (1 << pos); }
int Reset(int N, int pos) { return N = N & ~(1 << pos); }
bool Chkbit(int N, int pos) { return (bool)(N & (1 << pos)); }
bool isVowel(char ch) {
  ch = toupper(ch);
  if (ch == 'A' || ch == 'U' || ch == 'I' || ch == 'O' || ch == 'E')
    return true;
  return false;
}
bool isConst(char ch) {
  if (isalpha(ch) && !isVowel(ch)) return true;
  return false;
}
int toInt(string s) {
  int sm;
  stringstream ss(s);
  ss >> sm;
  return sm;
}
long long int toLlint(string s) {
  long long int sm;
  stringstream ss(s);
  ss >> sm;
  return sm;
}
long long int ar[200007], br[200007], Csum[200007], a[200007], b[200007];
struct z {
  long long int v, id;
};
z Tree[200007 * 4][2];
void Update(int id, int l, int r, int pos, int f, long long int val) {
  if (l == r) {
    Tree[id][f].v = val;
    Tree[id][f].id = l;
    return;
  }
  int mid = (l + r) / 2;
  int lft = 2 * id;
  int rgt = lft + 1;
  if (pos <= mid)
    Update(lft, l, mid, pos, f, val);
  else
    Update(rgt, mid + 1, r, pos, f, val);
  if (Tree[lft][f].v >= Tree[rgt][f].v) {
    Tree[id][f] = Tree[lft][f];
  } else {
    Tree[id][f] = Tree[rgt][f];
  }
  return;
}
z Query(int id, int l, int r, int st, int ed, int f) {
  if (l >= st && r <= ed) return Tree[id][f];
  int mid = (l + r) / 2;
  int lft = 2 * id;
  int rgt = lft + 1;
  if (ed <= mid)
    return Query(lft, l, mid, st, ed, f);
  else if (st > mid)
    return Query(rgt, mid + 1, r, st, ed, f);
  else {
    z a = Query(lft, l, mid, st, ed, f);
    z b = Query(rgt, mid + 1, r, st, ed, f);
    z c;
    if (a.v >= b.v) {
      c = a;
    } else {
      c = b;
    }
    return c;
  }
}
int n, m, N;
long long int Solve(int l, int r) {
  z a = Query(1, 1, N, l, r, 0);
  if (a.id == r) a = Query(1, 1, N, l, r - 1, 0);
  z b = Query(1, 1, N, a.id + 1, r, 1);
  long long int ans = a.v + b.v;
  a = Query(1, 1, N, l, r, 1);
  if (a.id == l) a = Query(1, 1, N, l + 1, r, 1);
  b = Query(1, 1, N, l, a.id - 1, 0);
  ans = max(ans, (a.v + b.v));
  return ans;
}
int main() {
  n = in<int>(), m = in<int>();
  for (int i = 1; i < n + 1; i++) ar[i] = in<long long int>();
  for (int i = 1; i < n + 1; i++) br[i] = in<long long int>();
  N = n * 2;
  for (int i = n + 1; i < N + 1; i++) ar[i] = ar[i - n], br[i] = br[i - n];
  long long int Sum = 0;
  for (int i = 1; i < N + 1; i++) {
    long long int a = 2 * br[i];
    long long int val = a - Sum;
    Update(1, 1, N, i, 0, val);
    val = a + Sum;
    Update(1, 1, N, i, 1, val);
    Sum += ar[i];
  }
  while (m--) {
    int a, b;
    a = in<int>(), b = in<int>();
    int l, r;
    if (a <= b) {
      l = b + 1, r = (n + a - 1);
    } else {
      l = b + 1, r = a - 1;
    }
    printf("%lld\n", Solve(l, r));
  }
  return 0;
}
