#include <bits/stdc++.h>
using namespace std;
struct node {
  long long lmost, rmost, v;
};
long long p;
node segt[1050000];
long long d[300005];
long long h[300005];
int n, m;
void init(int x, int l, int r) {
  segt[x].lmost = p;
  segt[x].rmost = -2000000000;
  segt[x].v = 0;
  if (l != r) {
    int k = (l + r) / 2;
    init(x * 2, l, k);
    init(x * 2 + 1, k + 1, r);
  }
}
void debug(int x, int l, int r) {
  cout << "index x = " << x << "\t: " << l << " " << r << "\t" << segt[x].lmost
       << " " << segt[x].rmost << " " << segt[x].v << endl;
  if (l != r) {
    int k = (l + r) / 2;
    debug(x * 2, l, k);
    debug(x * 2 + 1, k + 1, r);
  }
}
void insert(int i, long long d, long long h) {
  int x = 1, l = 1, r = n * 2, k;
  while (l != r) {
    segt[x].v = max(segt[x].v, d + h - segt[x].lmost);
    segt[x].lmost = min(segt[x].lmost, d - h);
    segt[x].rmost = max(segt[x].rmost, d + h);
    k = (l + r) / 2;
    if (i <= k) {
      r = k;
      x = x * 2;
    } else {
      l = k + 1;
      x = x * 2 + 1;
    }
  }
  segt[x].lmost = min(segt[x].lmost, d - h);
  segt[x].rmost = max(segt[x].rmost, d + h);
}
long long solve(int x, int l, int r, int i, int j, long long &t1,
                long long &t2) {
  if ((l == i) && (r == j)) {
    t1 = segt[x].lmost;
    t2 = segt[x].rmost;
    return segt[x].v;
  }
  int k = (l + r) / 2;
  if (j <= k) return solve(x * 2, l, k, i, j, t1, t2);
  if (i > k) return solve(x * 2 + 1, k + 1, r, i, j, t1, t2);
  long long l1, r1, l2, r2;
  long long res = max(solve(x * 2, l, k, i, k, l1, r1),
                      solve(x * 2 + 1, k + 1, r, k + 1, j, l2, r2));
  t1 = min(l1, l2);
  t2 = max(r1, r2);
  res = max(res, r2 - l1);
  return res;
}
int main() {
  cin >> n >> m;
  d[0] = 0;
  for (int i = 1; i <= n; ++i) {
    cin >> d[i];
    d[i] += d[i - 1];
  }
  p = d[n] * 4 + 2000000000;
  init(1, 1, n * 2);
  for (int i = 1; i <= n; ++i) {
    cin >> h[i];
    h[i] *= 2;
    insert(i, d[i - 1], h[i]);
  }
  for (int i = 1; i <= n; ++i) insert(n + i, d[n] + d[i - 1], h[i]);
  int a, b;
  long long t1, t2;
  for (int i = 0; i < m; ++i) {
    cin >> a >> b;
    if (a <= b)
      cout << solve(1, 1, n * 2, b + 1, a + n - 1, t1, t2) << endl;
    else
      cout << solve(1, 1, n * 2, b + 1, a - 1, t1, t2) << endl;
  }
  return 0;
}
