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 = 200005, P = 1000000007;
using ll = long long;
int n, q, a[N];
ll w[N];
struct BIT {
  ll c[N];
  bool mod;
  inline static int lowbit(int x) { return x & -x; }
  void add(int x, ll val) {
    while (x <= n) {
      c[x] += val;
      if (mod) c[x] %= P;
      x += lowbit(x);
    }
  }
  ll query(int x) {
    ll ret = 0;
    while (x) ret += c[x], x -= lowbit(x);
    return mod ? ret % P : ret;
  }
  inline ll query(int x, int y) { return query(y) - query(x - 1); }
} ta, tb;
int getpos(int l, int r) {
  int ans = l, lp = l;
  ll t = ta.query(l, r);
  while (l <= r) {
    int mid = (l + r) >> 1;
    if (ta.query(lp, mid) > t / 2)
      ans = mid, r = mid - 1;
    else
      l = mid + 1;
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> q;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) cin >> w[i];
  ta.mod = 0;
  tb.mod = 1;
  for (int i = 1; i <= n; i++) {
    a[i] -= i;
    ta.add(i, w[i]);
    tb.add(i, a[i] * w[i] % P);
  }
  for (int _ = 0; _ < q; _++) {
    int t1, t2;
    cin >> t1 >> t2;
    if (t1 < 0) {
      t1 = -t1;
      ta.add(t1, -w[t1]);
      tb.add(t1, a[t1] * -w[t1] % P);
      ta.add(t1, w[t1] = t2);
      tb.add(t1, a[t1] * w[t1] % P);
    } else {
      int k = getpos(t1, t2);
      ll ans = (ta.query(t1, k) % P * a[k] % P - tb.query(t1, k)) % P +
               (tb.query(k, t2) - ta.query(k, t2) % P * a[k] % P) % P;
      ans = (ans % P + P) % P;
      cout << ans << endl;
    }
  }
  return 0;
}