#include <bits/stdc++.h>
using namespace std;
const int maxn = 200 * 1000 + 7;
const int INF = 1000 * 1000 * 1000 + 7;
const long long LINF = 1LL * INF * INF;
long long h[maxn];
long long d[maxn];
struct node {
  long long plus;
  long long minus;
  long long ans;
  node(int i = 0) {
    plus = 2LL * h[i] + d[i];
    minus = 2LL * h[i] - d[i];
    ans = -INF;
  }
  node(long long a, long long b, long long c) {
    plus = a;
    minus = b;
    ans = c;
  }
  node operator+(const node& a) const {
    return node(max(plus, a.plus), max(minus, a.minus),
                max(max(ans, a.ans), minus + a.plus));
  }
} t[4 * maxn];
void build(int v, int tl, int tr) {
  if (tl == tr) {
    t[v] = node(tl);
    return;
  }
  int tm = (tl + tr) / 2;
  build(v + v, tl, tm);
  build(v + v + 1, tm + 1, tr);
  t[v] = t[v + v] + t[v + v + 1];
}
node ans(int v, int tl, int tr, int l, int r) {
  if (l > r) return node(-LINF, -LINF, -LINF);
  if (tl == l && tr == r) return t[v];
  int tm = (tl + tr) / 2;
  return ans(v + v, tl, tm, l, min(r, tm)) +
         ans(v + v + 1, tm + 1, tr, max(l, tm + 1), r);
}
int main() {
  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 = 0; i < n; i++) {
    d[i + n] = d[i];
    h[i + n] = h[i];
  }
  for (int i = 1; i < 2 * n; i++) d[i] += d[i - 1];
  for (int i = 2 * n - 1; i > 0; i--) {
    d[i] = d[i - 1];
  }
  d[0] = 0;
  build(1, 0, 2 * n - 1);
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    node res;
    if (a <= b) {
      res = ans(1, 0, 2 * n - 1, b + 1, a + n - 1);
    } else {
      res = ans(1, 0, 2 * n - 1, b + 1, a - 1);
    }
    cout << res.ans << endl;
  }
}
