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;
long long acum[301009], wacum[301009], aw[301009];
long long read(int i, long long *tree, int mod = -1) {
  long long ret = 0;
  while (i > 0) {
    ret += tree[i];
    if (mod != -1) ret %= 1000000007;
    i -= (i & -i);
  }
  return ret;
}
void add(int i, int v, long long *tree, int maxi, int mod = -1) {
  while (i <= maxi) {
    tree[i] += v;
    if (mod != -1) tree[i] %= 1000000007;
    i += (i & -i);
  }
}
long long query(int l, int r, long long *tree, int mod = -1) {
  if (l > r) return 0;
  long long ans = read(r, tree, mod) - read(l - 1, tree, mod);
  if (mod != -1) ans = (ans + 1000000007) % 1000000007;
  return ans;
}
int a[301009], w[301009];
int main() {
  int n, q, val, l, r, id;
  const int maxi = 200009;
  scanf("%d %d", &n, &q);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &w[i]);
    add(i, w[i], acum, maxi);
    add(i, (i * 1LL * w[i]) % 1000000007, wacum, maxi, 1000000007);
    add(i, (a[i] * 1LL * w[i]) % 1000000007, aw, maxi, 1000000007);
  }
  while (q--) {
    scanf("%d %d", &l, &r);
    if (l < 0) {
      id = -l;
      add(id, -w[id], acum, maxi);
      add(id, (1000000007 - (id * 1LL * w[id]) % 1000000007) % 1000000007,
          wacum, maxi, 1000000007);
      add(id, (1000000007 - (a[id] * 1LL * w[id]) % 1000000007) % 1000000007,
          aw, maxi, 1000000007);
      w[id] = r;
      add(id, w[id], acum, maxi);
      add(id, (id * 1LL * w[id]) % 1000000007, wacum, maxi, 1000000007);
      add(id, (a[id] * 1LL * w[id]) % 1000000007, aw, maxi, 1000000007);
    } else {
      int lo = l, hi = r;
      while (lo < hi) {
        int mid = (lo + hi + 1) / 2;
        long long p1 = query(l, mid - 1, acum);
        long long p2 = query(mid + 1, r, acum);
        if (p1 > p2 + w[mid]) {
          hi = mid - 1;
        } else
          lo = mid;
      }
      id = lo;
      int pos = a[id] - (id - l);
      long long ans = 0;
      ans -= query(l, id - 1, aw, 1000000007);
      ans = (ans + 1000000007) % 1000000007;
      ans += (query(l, id - 1, wacum, 1000000007) -
              l * 1LL * query(l, id - 1, acum, 1000000007)) %
             1000000007;
      ans = (ans + 1000000007) % 1000000007;
      ans += (pos * 1LL * query(l, id - 1, acum, 1000000007)) % 1000000007;
      ans = (ans + 1000000007) % 1000000007;
      ans += query(id + 1, r, aw, 1000000007);
      ans = (ans + 1000000007) % 1000000007;
      ans -= (query(id + 1, r, wacum, 1000000007) -
              (id)*1LL * query(id + 1, r, acum, 1000000007)) %
             1000000007;
      ans = (ans + 1000000007) % 1000000007;
      ans -= (a[id] * 1LL * query(id + 1, r, acum, 1000000007)) % 1000000007;
      ans = (ans + 1000000007) % 1000000007;
      printf("%lld\n", ans);
    }
  }
}