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 maxn = 2e5 + 10;
long long p[maxn], w[maxn];
long long c[maxn];
inline int lowbit(int s) { return s & (-s); }
inline void modify(int i, long long x, int n) {
  while (i <= n) c[i] += x, i += lowbit(i);
}
inline long long query(int i) {
  long long ret = 0;
  while (i > 0) ret += c[i], i -= lowbit(i);
  return ret;
}
long long C[2][maxn];
const long long mod = 1e9 + 7;
inline void Modify(int op, int i, long long x, int n) {
  x = (x % mod + mod) % mod;
  while (i <= n) C[op][i] = (C[op][i] + x) % mod, i += lowbit(i);
}
inline long long Query(int op, int i) {
  long long ret = 0;
  while (i > 0) ret = (ret + C[op][i]) % mod, i -= lowbit(i);
  return ret;
}
int main() {
  int n, q;
  scanf("%d %d", &n, &q);
  for (int i = 1; i <= n; ++i) scanf("%lld", p + i);
  for (int i = 1; i <= n; ++i) {
    scanf("%lld", w + i);
    modify(i, w[i], n);
    Modify(0, i, p[i] * w[i], n);
    Modify(1, i, i * w[i], n);
  }
  while (q--) {
    long long x, y;
    scanf("%lld %lld", &x, &y);
    if (x < 0) {
      x = -x;
      modify(x, -w[x], n);
      Modify(0, x, -p[x] * w[x], n);
      Modify(1, x, -x * w[x], n);
      w[x] = y;
      modify(x, w[x], n);
      Modify(0, x, p[x] * w[x], n);
      Modify(1, x, x * w[x], n);
    } else {
      long long tmp = query(x - 1);
      long long tot = query(y) - tmp;
      int l = x, r = y;
      while (l < r) {
        int mid = (l + r) / 2;
        long long now = query(mid) - tmp;
        if (now + now >= tot)
          r = mid;
        else
          l = mid + 1;
      }
      long long st = p[r] - (r - x);
      long long suml1 = (Query(1, r) + mod - Query(1, x - 1)) % mod;
      suml1 = (suml1 +
               (st - x + mod) % mod * ((query(r) + mod - tmp % mod) % mod)) %
              mod;
      long long suml2 = (Query(0, x - 1) + mod - Query(0, r)) % mod;
      st = p[r] + 1;
      long long sumr1 = (Query(0, y) + mod - Query(0, r)) % mod;
      long long sumr2 = (Query(1, y) + mod - Query(1, r)) % mod;
      sumr2 = (sumr2 + (st - (r + 1) + mod) % mod *
                           ((query(y) + mod - query(r) % mod) % mod)) %
              mod;
      sumr2 = (mod - sumr2) % mod;
      long long ans = (suml1 + suml2 + sumr1 + sumr2) % mod;
      printf("%lld\n", ans);
    }
  }
  return 0;
}