#include <bits/stdc++.h>
using namespace std;
template <class T>
inline T bigmod(T p, T e, T M) {
  long long ret = 1;
  for (; e > 0; e >>= 1) {
    if (e & 1) ret = (ret * p) % M;
    p = (p * p) % M;
  }
  return (T)ret;
}
template <class T>
inline T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <class T>
inline T modinverse(T a, T M) {
  return bigmod(a, M - 2, M);
}
template <class T>
inline T lcm(T a, T b) {
  a = abs(a);
  b = abs(b);
  return (a / gcd(a, b)) * b;
}
template <class T, class X>
inline bool getbit(T a, X i) {
  T t = 1;
  return ((a & (t << i)) > 0);
}
template <class T, class X>
inline T setbit(T a, X i) {
  T t = 1;
  return (a | (t << i));
}
template <class T, class X>
inline T resetbit(T a, X i) {
  T t = 1;
  return (a & (~(t << i)));
}
inline long long power(long long a, long long b) {
  long long multiply = 1;
  for (int i = (0); i < (b); i++) {
    multiply *= a;
  }
  return multiply;
}
struct info {
  long long left, right;
  long long ans;
  info() {}
  info(long long l, long long r, long long a) {
    left = l;
    right = r;
    ans = a;
  }
} tree[600005];
long long d[200005], h[200005], sum[200005];
info merge(info leftNode, info rightNode) {
  info node;
  node.left = max(leftNode.left, rightNode.left);
  node.right = max(leftNode.right, rightNode.right);
  node.ans =
      max(leftNode.left + rightNode.right, leftNode.right + rightNode.left);
  node.ans = max(node.ans, max(leftNode.ans, rightNode.ans));
  return node;
}
void build(int node, int l, int r) {
  if (l == r) {
    tree[node].left = 2 * h[l] - sum[l];
    tree[node].right = 2 * h[l] + sum[l];
    tree[node].ans = -1e15;
  }
  if (l >= r) return;
  int mid = (l + r) / 2;
  build(node * 2, l, mid);
  build(node * 2 + 1, mid + 1, r);
  tree[node] = merge(tree[node * 2], tree[node * 2 + 1]);
}
info query(int node, int l, int r, int x, int y) {
  info temp;
  if (x > r || y < l) return info(-1e15, -1e15, -1e15);
  if (x <= l && r <= y) return tree[node];
  int mid = (l + r) / 2;
  info L = query(node * 2, l, mid, x, y);
  info R = query(node * 2 + 1, mid + 1, r, x, y);
  temp = merge(L, R);
  return temp;
}
int main() {
  ios_base::sync_with_stdio(0);
  int n, m;
  cin >> n >> m;
  for (int i = (1); i < (n + 1); i++) {
    cin >> d[i];
    d[i + n] = d[i];
  }
  for (int i = (1); i < (n + 1); i++) {
    cin >> h[i];
    h[i + n] = h[i];
  }
  for (int i = (1); i < (2 * n + 1); i++) sum[i] = sum[i - 1] + d[i - 1];
  build(1, 1, 2 * n);
  for (int i = (0); i < (m); i++) {
    int a, b;
    cin >> a >> b;
    if (a <= b)
      cout << query(1, 1, 2 * n, b + 1, a - 1 + n).ans << endl;
    else
      cout << query(1, 1, 2 * n, b + 1, a - 1).ans << endl;
  }
  return 0;
}
