Problem: There is an infinite line consisting of cells. There are n boxes in some cells of this line. The i-th box stands in the cell a_i and has weight w_i. All a_i are distinct, moreover, a_{i - 1} < a_i holds for all valid i.

You would like to put together some boxes. Putting together boxes with indices in the segment [l, r] means that you will move some of them in such a way that their positions will form some segment [x, x + (r - l)].

In one step you can move any box to a neighboring cell if it isn't occupied by another box (i.e. you can choose i and change a_i by 1, all positions should remain distinct). You spend w_i units of energy moving the box i by one cell. You can move any box any number of times, in arbitrary order.

Sometimes weights of some boxes change, so you have queries of two types: 

  1. id nw — weight w_{id} of the box id becomes nw. 
  2. l r — you should compute the minimum total energy needed to put together boxes with indices in [l, r]. Since the answer can be rather big, print the remainder it gives when divided by 1000 000 007 = 10^9 + 7. Note that the boxes are not moved during the query, you only should compute the answer. 



Note that you should minimize the answer, not its remainder modulo 10^9 + 7. So if you have two possible answers 2 ⋅ 10^9 + 13 and 2 ⋅ 10^9 + 14, you should choose the first one and print 10^9 + 6, even though the remainder of the second answer is 0.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^5) — the number of boxes and the number of queries.

The second line contains n integers a_1, a_2, ... a_n (1 ≤ a_i ≤ 10^9) — the positions of the boxes. All a_i are distinct, a_{i - 1} < a_i holds for all valid i.

The third line contains n integers w_1, w_2, ... w_n (1 ≤ w_i ≤ 10^9) — the initial weights of the boxes.

Next q lines describe queries, one query per line.

Each query is described in a single line, containing two integers x and y. If x < 0, then this query is of the first type, where id = -x, nw = y (1 ≤ id ≤ n, 1 ≤ nw ≤ 10^9). If x > 0, then the query is of the second type, where l = x and r = y (1 ≤ l_j ≤ r_j ≤ n). x can not be equal to 0.

Output

For each query of the second type print the answer on a separate line. Since answer can be large, print the remainder it gives when divided by 1000 000 007 = 10^9 + 7.

Example

Input

5 8
1 2 6 7 10
1 1 1 1 2
1 1
1 5
1 3
3 5
-3 5
-1 10
1 4
2 5


Output

0
10
3
4
18
7

Note

Let's go through queries of the example: 

  1. 1\ 1 — there is only one box so we don't need to move anything. 
  2. 1\ 5 — we can move boxes to segment [4, 8]: 1 ⋅ |1 - 4| + 1 ⋅ |2 - 5| + 1 ⋅ |6 - 6| + 1 ⋅ |7 - 7| + 2 ⋅ |10 - 8| = 10. 
  3. 1\ 3 — we can move boxes to segment [1, 3]. 
  4. 3\ 5 — we can move boxes to segment [7, 9]. 
  5. -3\ 5 — w_3 is changed from 1 to 5. 
  6. -1\ 10 — w_1 is changed from 1 to 10. The weights are now equal to w = [10, 1, 5, 1, 2]. 
  7. 1\ 4 — we can move boxes to segment [1, 4]. 
  8. 2\ 5 — we can move boxes to segment [5, 8]. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
mt19937 rnd(228);
const int N = 2e5 + 7;
const int M = 1e9 + 7;
long long f_w[N];
long long f_aw[N];
void inc_w(int x, int y) {
  for (; x < N; x = (x | (x + 1))) {
    f_w[x] += y;
  }
}
void inc_aw(int x, long long y) {
  y %= M;
  if (y < 0) y += M;
  for (; x < N; x = (x | (x + 1))) {
    f_aw[x] += y;
    if (f_aw[x] >= M) {
      f_aw[x] -= M;
    }
  }
}
long long get_w(int x) {
  long long res = 0;
  for (; x >= 0; x = (x & (x + 1)) - 1) {
    res += f_w[x];
  }
  return res;
}
int get_aw(int x) {
  int res = 0;
  for (; x >= 0; x = (x & (x + 1)) - 1) {
    res += f_aw[x];
    if (res >= M) res -= M;
  }
  return res;
}
long long get_w(int l, int r) { return get_w(r) - get_w(l - 1); }
int get_aw(int l, int r) {
  int res = get_aw(r);
  res -= get_aw(l - 1);
  if (res < 0) res += M;
  return res;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, q;
  cin >> n >> q;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i] -= i;
  }
  vector<int> w(n);
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    inc_w(i, w[i]);
    inc_aw(i, a[i] * (long long)w[i]);
  }
  while (q--) {
    int x, y;
    cin >> x >> y;
    if (x < 0) {
      x = -x;
      x--;
      inc_w(x, -w[x]);
      inc_aw(x, -(a[x] * (long long)w[x]));
      w[x] = y;
      inc_w(x, w[x]);
      inc_aw(x, (a[x] * (long long)w[x]));
    } else {
      x--, y--;
      long long sum = get_w(x, y);
      long long need = sum / 2 + get_w(x - 1);
      int l = x - 1, r = y;
      while (l < r - 1) {
        int m = (l + r) / 2;
        if (get_w(m) <= need) {
          l = m;
        } else {
          r = m;
        }
      }
      int p = l + 1;
      long long ans = -get_aw(x, p) + get_aw(p + 1, y);
      if (ans < 0) ans += M;
      ans += (get_w(x, p) % M * (long long)a[p]) % M;
      if (ans >= M) ans -= M;
      ans -= (get_w(p + 1, y) % M * (long long)a[p]) % M;
      if (ans < 0) ans += M;
      cout << ans << '\n';
    }
  }
}