#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long x = 0, f = 1, c = getchar();
  while (c > '9' || c < '0') f = c == '-' ? -1 : 1, c = getchar();
  while (c >= '0' && c <= '9') x = x * 10 + c - 48, c = getchar();
  return x * f;
}
void write(long long x) {
  if (x < 0) putchar('-'), write(-x);
  if (x >= 10) write(x / 10);
  putchar(x % 10 + 48);
}
const int maxn = 6e5 + 50;
long long h[maxn], d[maxn];
int n, m, N;
struct tree {
  long long a, b, c;
  tree() { a = b = c = 0; }
} t[maxn << 2];
tree merge(tree &ls, tree &rs) {
  tree ret;
  ret.a = max(ls.a, rs.a);
  ret.b = max(ls.b, rs.b);
  ret.c = max(ls.c, rs.c);
  ret.c = max(ret.c, ls.b + rs.a);
  return ret;
}
void build(int k, int l, int r) {
  if (l == r) {
    t[k].c = 0;
    t[k].a = 2 * h[l] + d[l - 1];
    t[k].b = 2 * h[l] - d[l - 1];
    return;
  }
  int mid = l + r >> 1;
  build(k << 1, l, mid);
  build(k << 1 | 1, mid + 1, r);
  t[k] = merge(t[k << 1], t[k << 1 | 1]);
}
tree query(int k, int l, int r, int x, int y) {
  if (x == l && r == y) return t[k];
  int mid = l + r >> 1;
  if (y <= mid)
    return query(k << 1, l, mid, x, y);
  else if (x > mid)
    return query(k << 1 | 1, mid + 1, r, x, y);
  else {
    tree L = query(k << 1, l, mid, x, mid),
         R = query(k << 1 | 1, mid + 1, r, mid + 1, y);
    tree ret = merge(L, R);
    return ret;
  }
}
int main() {
  n = read(), m = read();
  for (int i = 1; i <= n; i++) d[i] = d[i + n] = read();
  for (int i = 1; i <= n; i++) h[i] = h[i + n] = read();
  N = n << 1;
  for (int i = 2; i <= N; i++) d[i] = d[i - 1] + d[i];
  build(1, 1, N);
  while (m--) {
    int u = read(), v = read();
    swap(u, v);
    if (u < v)
      u++, v--;
    else
      u++, v = v + n - 1;
    write(query(1, 1, N, u, v).c), putchar(10);
  }
  return 0;
}
