#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100010;
const int MAXBOX = 100010;
const int BLEN = 400;
int d[MAXN];
long long h[2 * MAXN], ps[2 * MAXN];
long long mxDec[MAXBOX], mxAdd[MAXBOX], inside[MAXBOX];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < n; i++) cin >> d[i];
  for (int i = 0; i < n; i++) cin >> h[i];
  for (int i = n; i < 2 * n; i++) h[i] = h[i - n];
  for (int i = 0; i < 2 * n; i++) ps[i + 1] = ps[i] + d[i % n];
  int mxBox = (2 * n - 1) / BLEN;
  for (int i = 0; i <= mxBox; i++) {
    int l = i * BLEN;
    int r = min(2 * n - 1, (i + 1) * BLEN);
    mxDec[i] = 2 * h[l] - ps[l];
    mxAdd[i] = 2 * h[l] + ps[l];
    for (int j = l + 1; j < r; j++) {
      inside[i] = max(inside[i], mxDec[i] + 2 * h[j] + ps[j]);
      mxDec[i] = max(mxDec[i], 2 * h[j] - ps[j]);
      mxAdd[i] = max(mxAdd[i], 2 * h[j] + ps[j]);
    }
  }
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    a--, b++;
    swap(a, b);
    if (a > b) b += n;
    int boxa = a / BLEN;
    int boxb = b / BLEN;
    long long ans = 0;
    if (boxa == boxb) {
      long long mxd = 2 * h[a] - ps[a];
      for (int j = a + 1; j <= b; j++) {
        ans = max(ans, mxd + 2 * h[j] + ps[j]);
        mxd = max(mxd, 2 * h[j] - ps[j]);
      }
    } else {
      long long mxd = 2 * h[a] - ps[a];
      for (int j = a + 1; j / BLEN == boxa; j++) {
        ans = max(ans, mxd + 2 * h[j] + ps[j]);
        mxd = max(mxd, 2 * h[j] - ps[j]);
      }
      for (int j = boxa + 1; j < boxb; j++) {
        ans = max(ans, inside[j]);
        ans = max(ans, mxAdd[j] + mxd);
        mxd = max(mxd, mxDec[j]);
      }
      for (int j = b - (b % BLEN); j <= b; j++) {
        ans = max(ans, mxd + 2 * h[j] + ps[j]);
        mxd = max(mxd, 2 * h[j] - ps[j]);
      }
    }
    cout << ans << "\n";
  }
}
