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;
int n, q;
const int maxn = 2e5 + 5, md = 1e9 + 7;
int pos[maxn], wei[maxn];
struct Fenwick_Tree {
  long long c[maxn];
  void add(int p, int x) {
    for (; p <= n; p += p & (-p)) c[p] = (c[p] + x);
  }
  long long s(int p) {
    long long result = 0;
    for (; p; p -= p & (-p)) result = (result + c[p]);
    return result;
  }
  long long s2(int p) {
    long long result = 0;
    for (; p; p -= p & (-p)) result = (result + c[p]) % md;
    return result;
  }
} tr, tr2;
signed main() {
  scanf("%d%d", &n, &q);
  for (int i = (1); i <= (n); ++i) scanf("%d", pos + i), pos[i] = (pos[i] - i);
  for (int i = (1); i <= (n); ++i) {
    scanf("%d", wei + i);
    tr.add(i, wei[i]);
    tr2.add(i, 1ll * wei[i] * pos[i] % md);
  }
  long long ans = 0;
  for (int i = (1); i <= (q); ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    if (a < 0) {
      a = -a;
      tr.add(a, -wei[a]);
      tr2.add(a, -1ll * wei[a] * pos[a] % md);
      tr.add(a, b);
      tr2.add(a, b * 1ll * pos[a] % md);
      wei[a] = b;
    } else {
      int l = a - 1, r = b, mid;
      while (r - l > 1) {
        mid = (l + r) >> 1;
        if (tr.s(mid) - tr.s(a - 1) < tr.s(b) - tr.s(mid)) {
          l = mid;
        } else {
          r = mid;
        }
      }
      ans = 1ll * (tr.s2(r) - tr.s2(a - 1) - (tr.s2(b) - tr.s2(r - 1))) % md *
            pos[r] % md;
      ans %= md;
      ans +=
          (tr2.s2(b) - tr2.s2(r - 1)) % md - (tr2.s2(r) - tr2.s2(a - 1)) % md;
      ans %= md;
      ans = (ans + md) % md;
      printf("%lld\n", ans);
    }
  }
  return 0;
}