#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e18;
const int N = 2e5 + 8;
const int K = 18;
int n, q;
long long d[N], h[N], cum[N];
pair<pair<long long, int>, pair<long long, int> > st[2][N][K];
pair<pair<long long, int>, pair<long long, int> > combine(
    pair<pair<long long, int>, pair<long long, int> > l,
    pair<pair<long long, int>, pair<long long, int> > r) {
  if (l.first == r.first) return max(l, r);
  if (l < r) swap(l, r);
  return make_pair(l.first, max(l.second, r.first));
}
void build() {
  for (int i = 1; i <= 2 * n; i++) {
    st[0][i][0] =
        make_pair(make_pair(2 * h[i] + cum[i], i), make_pair(-INF, -1));
    st[1][i][0] =
        make_pair(make_pair(2 * h[i] - cum[i], i), make_pair(-INF, -1));
  }
  for (int k = 1; k < K; k++)
    for (int i = 1; i <= 2 * n; i++) {
      int id = i + (1 << (k - 1));
      if (id > 2 * n) {
        st[0][i][k] = st[0][i][k - 1];
        st[1][i][k] = st[1][i][k - 1];
        continue;
      }
      st[0][i][k] = combine(st[0][i][k - 1], st[0][id][k - 1]);
      st[1][i][k] = combine(st[1][i][k - 1], st[1][id][k - 1]);
    }
}
long long query(int l, int r) {
  int k = 31 - __builtin_clz(r - l + 1);
  pair<pair<long long, int>, pair<long long, int> > a =
      combine(st[0][l][k], st[0][r - (1 << k) + 1][k]);
  pair<pair<long long, int>, pair<long long, int> > b =
      combine(st[1][l][k], st[1][r - (1 << k) + 1][k]);
  if (a.first.second != b.first.second) return a.first.first + b.first.first;
  return max(a.first.first + b.second.first, a.second.first + b.first.first);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> q;
  for (int i = 2; i <= n + 1; i++) cin >> d[i], d[i + n] = d[i];
  d[1] = d[n + 1];
  for (int i = 1; i <= n; i++) cin >> h[i], h[i + n] = h[i];
  for (int i = 1; i <= 2 * n; i++) cum[i] = cum[i - 1] + d[i];
  build();
  while (q--) {
    int l, r;
    cin >> l >> r;
    if (l <= r)
      cout << query(r + 1, l + n - 1) << '\n';
    else
      cout << query(r + 1, l - 1) << '\n';
  }
}
