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 = 200100, mod = 1000000007;
inline void reduce(int& x) { x += x >> 31 & mod; }
long long sum[N];
int sum2[N];
int n, q, a[N], b[N], mx;
long long qry(int x) {
  long long ret = 0;
  for (; x; x -= x & -x) ret += sum[x];
  return ret;
}
int qry2(int x) {
  int ret = 0;
  for (; x; x -= x & -x) reduce(ret += sum2[x] - mod);
  return ret;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> q;
  for (; (1 << mx) <= n; ++mx)
    ;
  --mx;
  for (int i = 1; i <= n; ++i) cin >> a[i], a[i] -= i;
  for (int i = 1; i <= n; ++i) cin >> b[i];
  for (int i = 1; i <= n; ++i) {
    sum[i] += b[i];
    sum2[i] = (sum2[i] + (long long)a[i] * b[i]) % mod;
    if (i + (i & -i) <= n)
      sum[i + (i & -i)] += sum[i], reduce(sum2[i + (i & -i)] += sum2[i] - mod);
  }
  for (; q-- > 0;) {
    int x, y;
    cin >> x >> y;
    if (x < 0) {
      x = -x;
      int delta = (long long)(y - b[x] - mod) * a[x] % mod;
      for (int j = x; j <= n; j += j & -j)
        sum[j] += y - b[x], reduce(sum2[j] += delta);
      b[x] = y;
    } else {
      long long w = qry(x - 1) + qry(y);
      int now = 0;
      for (int j = mx; ~j; --j)
        if (now + (1 << j) <= n && w >= 2 * sum[now + (1 << j)])
          w -= 2 * sum[now += 1 << j];
      int ans = (qry2(y) + qry2(x - 1) - 2 * qry2(now) - w * a[now + 1]) % mod;
      reduce(ans);
      cout << ans << '\n';
    }
  }
  return 0;
}