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 MOD = int(1e9) + 7;
int norm(int a) {
  if (a >= MOD) a -= MOD;
  if (a < 0) a += MOD;
  return a;
}
int norm(const long long &a) { return norm(int(a % MOD)); }
int mul(int a, int b) { return int((a * 1ll * b) % MOD); }
const int N = 200 * 1000 + 555;
int n, q;
int a[N], w[N];
inline bool read() {
  if (!(cin >> n >> q)) return false;
  for (int i = int(0); i < int(n); i++) assert(scanf("%d", &a[i]) == 1);
  for (int i = int(0); i < int(n); i++) assert(scanf("%d", &w[i]) == 1);
  return true;
}
long long fW[N], fAW[N];
void inc(long long f[N], int pos, long long val) {
  for (; pos < N; pos |= pos + 1) f[pos] += val;
}
long long sum(long long f[N], int pos) {
  long long ans = 0;
  for (; pos >= 0; pos = (pos & (pos + 1)) - 1) ans += f[pos];
  return ans;
}
long long getSum(long long f[N], int l, int r) {
  return sum(f, r - 1) - sum(f, l - 1);
}
int getNSum(long long f[N], int l, int r) {
  return norm(sum(f, r - 1) - sum(f, l - 1));
}
inline void solve() {
  for (int i = int(0); i < int(n); i++) {
    a[i] -= i;
    inc(fW, i, w[i]);
    inc(fAW, i, mul(a[i], w[i]));
  }
  for (int _ = int(0); _ < int(q); _++) {
    int x, y;
    assert(scanf("%d%d", &x, &y) == 2);
    if (x < 0) {
      x = -x - 1;
      inc(fW, x, -w[x]);
      inc(fAW, x, -mul(a[x], w[x]));
      w[x] = y;
      inc(fW, x, w[x]);
      inc(fAW, x, mul(a[x], w[x]));
    } else {
      x--;
      long long sum = getSum(fW, x, y);
      int lf = x, rg = y;
      while (rg - lf > 1) {
        int mid = (lf + rg) >> 1;
        if (2 * getSum(fW, x, mid) > sum)
          rg = mid;
        else
          lf = mid;
      }
      assert(x <= lf && lf < y);
      int ans = norm(mul(a[lf], getNSum(fW, x, lf)) - getNSum(fAW, x, lf));
      ans = norm(ans +
                 norm(getNSum(fAW, lf, y) - mul(a[lf], getNSum(fW, lf, y))));
      printf("%d\n", ans);
    }
  }
}
int main() {
  cout << fixed << setprecision(15);
  if (read()) {
    solve();
  }
  return 0;
}