#include <bits/stdc++.h>
const int N = 200005;
using namespace std;
pair<long long, long long> MN = {LLONG_MAX, LLONG_MAX},
                           MX = {LLONG_MIN, LLONG_MIN};
long long n, m, d[N], h[N], s[N];
pair<pair<long long, long long>, pair<long long, long long> > A[4 * N],
    B[4 * N];
pair<pair<long long, long long>, pair<long long, long long> > combmx(
    pair<pair<long long, long long>, pair<long long, long long> > &a,
    pair<pair<long long, long long>, pair<long long, long long> > &b) {
  vector<pair<long long, long long> > vals = {a.first, a.second, b.first,
                                              b.second};
  sort(vals.begin(), vals.end());
  return {vals[3], vals[2]};
}
pair<pair<long long, long long>, pair<long long, long long> > combmn(
    pair<pair<long long, long long>, pair<long long, long long> > &a,
    pair<pair<long long, long long>, pair<long long, long long> > &b) {
  vector<pair<long long, long long> > vals = {a.first, a.second, b.first,
                                              b.second};
  sort(vals.begin(), vals.end());
  return {vals[0], vals[1]};
}
void build(int i, int l, int r) {
  if (l == r) {
    A[i] = {{2 * h[l] + s[l - 1], l}, MX};
    B[i] = {{2 * h[l] - s[l - 1], l}, MX};
    return;
  }
  int m = (l + r) / 2;
  build(i * 2, l, m);
  build(i * 2 + 1, m + 1, r);
  A[i] = combmx(A[i * 2], A[i * 2 + 1]);
  B[i] = combmx(B[i * 2], B[i * 2 + 1]);
}
pair<pair<long long, long long>, pair<long long, long long> > getmx(
    int i, int l, int r, int se, int en) {
  if (se <= l && r <= en) {
    return A[i];
  }
  if (l > en || r < se) return {MX, MX};
  int m = (l + r) / 2;
  pair<pair<long long, long long>, pair<long long, long long> > v1 =
      getmx(i * 2, l, m, se, en);
  pair<pair<long long, long long>, pair<long long, long long> > v2 =
      getmx(i * 2 + 1, m + 1, r, se, en);
  return combmx(v1, v2);
}
pair<pair<long long, long long>, pair<long long, long long> > getmn(
    int i, int l, int r, int se, int en) {
  if (se <= l && r <= en) {
    return B[i];
  }
  if (l > en || r < se) return {MX, MX};
  int m = (l + r) / 2;
  pair<pair<long long, long long>, pair<long long, long long> > v1 =
      getmn(i * 2, l, m, se, en);
  pair<pair<long long, long long>, pair<long long, long long> > v2 =
      getmn(i * 2 + 1, m + 1, r, se, en);
  return combmx(v1, v2);
}
long long G(pair<long long, long long> &a, pair<long long, long long> &b) {
  if (a.second == b.second) return 0;
  return a.first + b.first;
}
int main() {
  ios_base::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    cin >> d[i];
    s[i] = s[i - 1] + d[i];
  }
  for (int i = 1; i <= n; i++) cin >> h[i];
  for (int i = 1; i <= n; i++) {
    s[i + n] = s[i + n - 1] + d[i];
    h[i + n] = h[i];
  }
  build(1, 1, 2 * n);
  while (m--) {
    int l, r;
    cin >> l >> r;
    pair<pair<long long, long long>, pair<long long, long long> > v1, v2;
    if (l <= r) {
      v1 = getmx(1, 1, 2 * n, r + 1, l + n - 1);
      v2 = getmn(1, 1, 2 * n, r + 1, l + n - 1);
    } else {
      v1 = getmx(1, 1, 2 * n, r + 1, l - 1);
      v2 = getmn(1, 1, 2 * n, r + 1, l - 1);
    }
    long long ans = 0;
    ans = max(ans, G(v1.first, v2.first));
    ans = max(ans, G(v1.second, v2.first));
    ans = max(ans, G(v1.second, v2.second));
    ans = max(ans, G(v1.first, v2.second));
    cout << ans << '\n';
  }
  return 0;
}
