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;
const int N = 222222;
const int MO = 1e9 + 7;
int n, a[N], w[N];
long long t[N << 2], e[N << 2];
void build(int k = 1, int l = 1, int r = n) {
  if (l == r) {
    t[k] = w[l];
    e[k] = (long long)a[l] * w[l] % MO;
    return;
  }
  int h = l + r >> 1;
  build(k << 1, l, h);
  build(k << 1 | 1, h + 1, r);
  t[k] = t[k << 1] + t[k << 1 | 1];
  e[k] = (e[k << 1] + e[k << 1 | 1]) % MO;
}
void modify(int x, int y, int k = 1, int l = 1, int r = n) {
  if (l == r) {
    t[k] = w[x];
    e[k] = (long long)a[x] * w[x] % MO;
    return;
  }
  int h = l + r >> 1;
  if (x <= h)
    modify(x, y, k << 1, l, h);
  else
    modify(x, y, k << 1 | 1, h + 1, r);
  t[k] = t[k << 1] + t[k << 1 | 1];
  e[k] = (e[k << 1] + e[k << 1 | 1]) % MO;
}
int query1(long long s, int k = 1, int l = 1, int r = n) {
  if (l == r) return l;
  int h = l + r >> 1;
  if (s <= t[k << 1] * 2) return query1(s, k << 1, l, h);
  return query1(s - t[k << 1] * 2, k << 1 | 1, h + 1, r);
}
long long query2(int L, int R, int k = 1, int l = 1, int r = n) {
  if (L > R) return 0;
  if (L <= l && r <= R) return t[k];
  int h = l + r >> 1;
  long long s = 0;
  if (L <= h) s += query2(L, R, k << 1, l, h);
  if (h < R) s += query2(L, R, k << 1 | 1, h + 1, r);
  return s;
}
long long query3(int L, int R, int k = 1, int l = 1, int r = n) {
  if (L > R) return 0;
  if (L <= l && r <= R) return e[k];
  int h = l + r >> 1;
  long long s = 0;
  if (L <= h) s += query3(L, R, k << 1, l, h);
  if (h < R) s += query3(L, R, k << 1 | 1, h + 1, r);
  return s % MO;
}
int main() {
  int i, q, x, y;
  long long s, r;
  scanf("%d%d", &n, &q);
  for (i = 1; i <= n; i = i + 1) scanf("%d", a + i), a[i] -= i;
  for (i = 1; i <= n; i = i + 1) scanf("%d", w + i);
  build();
  while (q--) {
    scanf("%d%d", &x, &y);
    if (x < 0) {
      x = -x;
      w[x] = y;
      modify(x, y);
    } else {
      s = query2(1, x - 1) * 2 + query2(x, y);
      i = query1(s);
      s = query3(i, y) - query2(i, y) % MO * a[i] % MO;
      r = query2(x, i) % MO * a[i] % MO - query3(x, i);
      cout << (s + r + (long long)MO * 10) % MO << endl;
    }
  }
  return 0;
}