#include <bits/stdc++.h>
using namespace std;
const int N = 200005;
long long a[N], b[N], c[N], d[N];
pair<int, int> tree[4 * N];
void build(int idx, int st, int nd) {
  if (st == nd) {
    tree[idx] = {st, st};
  } else {
    int mid = (st + nd) >> 1;
    build(1 + (idx << 1), st, mid);
    build(2 + (idx << 1), mid + 1, nd);
    tree[idx].first =
        c[tree[1 + (idx << 1)].first] >= c[tree[2 + (idx << 1)].first]
            ? tree[1 + (idx << 1)].first
            : tree[2 + (idx << 1)].first;
    tree[idx].second =
        d[tree[1 + (idx << 1)].second] >= d[tree[2 + (idx << 1)].second]
            ? tree[1 + (idx << 1)].second
            : tree[2 + (idx << 1)].second;
  }
}
int lq, rq, pos;
int val1, val2;
int get(int idx, int st, int nd, bool f) {
  if (lq <= st && nd <= rq) {
    return f ? tree[idx].first : tree[idx].second;
  }
  int mid = (st + nd) >> 1;
  if (rq <= mid) {
    return get(1 + (idx << 1), st, mid, f);
  }
  if (lq > mid) {
    return get(2 + (idx << 1), mid + 1, nd, f);
  }
  int t1 = get(1 + (idx << 1), st, mid, f),
      t2 = get(2 + (idx << 1), mid + 1, nd, f);
  return f ? c[t1] >= c[t2] ? t1 : t2 : d[t1] >= d[t2] ? t1 : t2;
}
int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &a[i]);
  }
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &b[i]);
  }
  for (int i = n; i < n + n; i++) {
    a[i] = a[i - n];
    b[i] = b[i - n];
  }
  for (int i = 1; i < n + n; i++) {
    a[i] += a[i - 1];
    c[i] = b[i] * 2 - a[i - 1];
    d[i] = b[i] * 2 + a[i - 1];
  }
  int nn = n + n;
  build(0, 0, nn - 1);
  while (m--) {
    int x, y;
    scanf("%d %d", &x, &y);
    x--;
    y--;
    if (x <= y) {
      lq = y + 1;
      rq = n + x - 1;
    } else {
      lq = y + 1;
      rq = x - 1;
    }
    pos = get(0, 0, nn - 1, true);
    int tmpl = lq, tmpr = rq;
    rq = pos - 1;
    int t1 = -1;
    if (lq <= rq) {
      t1 = get(0, 0, nn - 1, false);
    }
    int t2 = -1;
    lq = pos + 1;
    rq = tmpr;
    if (lq <= rq) {
      t2 = get(0, 0, nn - 1, false);
    }
    int pos2;
    if (t1 != -1 && t2 != -1) {
      pos2 = d[t1] >= d[t2] ? t1 : t2;
    } else if (t1 == -1) {
      pos2 = t2;
    } else {
      pos2 = t1;
    }
    if (pos > pos2) {
      swap(pos, pos2);
    }
    long long hold = c[pos] + d[pos2];
    lq = tmpl;
    rq = tmpr;
    pos2 = get(0, 0, nn - 1, false);
    rq = pos2 - 1;
    t1 = -1;
    if (lq <= rq) {
      t1 = get(0, 0, nn - 1, true);
    }
    t2 = -1;
    lq = pos2 + 1;
    rq = tmpr;
    if (lq <= rq) {
      t2 = get(0, 0, nn - 1, true);
    }
    if (t1 != -1 && t2 != -1) {
      pos = c[t1] >= c[t2] ? t1 : t2;
    } else if (t1 == -1) {
      pos = t2;
    } else {
      pos = t1;
    }
    if (pos > pos2) {
      swap(pos, pos2);
    }
    printf("%I64d\n", max(hold, c[pos] + d[pos2]));
  }
  return 0;
}
