#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, const U &b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, const U &b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T1, class T2>
inline void gn(T1 &x1, T2 &x2) {
  gn(x1), gn(x2);
}
template <class T1, class T2, class T3>
inline void gn(T1 &x1, T2 &x2, T3 &x3) {
  gn(x1, x2), gn(x3);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T1, class T2>
inline void print(T1 x1, T2 x2) {
  printsp(x1), println(x2);
}
template <class T1, class T2, class T3>
inline void print(T1 x1, T2 x2, T3 x3) {
  printsp(x1), printsp(x2), println(x3);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = (long long)a * a % m)
    if (b & 1) ans = (long long)ans * a % m;
  return ans;
}
long long d[200010], h[200010], first[200010], second[200010];
long long mn[800010], mx[800010], ans[800010];
void push_up(int u) {
  ans[u] = max(ans[(u << 1)], ans[((u << 1) | 1)]);
  smax(ans[u], mx[((u << 1) | 1)] - mn[(u << 1)]);
  mx[u] = max(mx[(u << 1)], mx[((u << 1) | 1)]);
  mn[u] = min(mn[(u << 1)], mn[((u << 1) | 1)]);
}
void build(int u, int L, int R) {
  if (L + 1 == R) {
    mn[u] = first[L];
    mx[u] = second[L];
    return;
  }
  build((u << 1), L, (L + R >> 1));
  build(((u << 1) | 1), (L + R >> 1), R);
  push_up(u);
}
long long sum, Mn;
void calc(int u, int L, int R, int l, int r) {
  smax(l, L);
  smin(r, R);
  if (l >= r) return;
  if (l == L && r == R) {
    smax(sum, max(ans[u], mx[u] - Mn));
    smin(Mn, mn[u]);
    return;
  }
  calc((u << 1), L, (L + R >> 1), l, r);
  calc(((u << 1) | 1), (L + R >> 1), R, l, r);
}
int main() {
  int n, m;
  gn(n, m);
  for (int i = 1; i <= n; i++) {
    gn(d[i]);
    d[n + i] = d[i];
  }
  for (int i = 1; i <= n; i++) {
    gn(h[i]);
    h[n + i] = h[i];
  }
  int N = n << 1;
  long long s = 0;
  for (int i = 1; i <= N; i++) {
    first[i] = s - 2 * h[i];
    second[i] = s + 2 * h[i];
    s += d[i];
  }
  build(1, 1, N + 1);
  while (m--) {
    int L, R;
    gn(L, R);
    if (L > R) R += n;
    sum = 0;
    Mn = 0x3f3f3f3f3f3f3f3fLL;
    calc(1, 1, N + 1, R + 1, L + n);
    println(sum);
  }
}
