438_D. The Child and Sequence

At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite sequence of Picks.

Fortunately, Picks remembers how to repair the sequence. Initially he should create an integer array a[1], a[2], ..., a[n]. Then he should perform a sequence of m operations. An operation can be one of the following:

  1. Print operation l, r. Picks should write down the value of <image>. 
  2. Modulo operation l, r, x. Picks should perform assignment a[i] = a[i] mod x for each i (l ≤ i ≤ r). 
  3. Set operation k, x. Picks should set the value of a[k] to x (in other words perform an assignment a[k] = x). 



Can you help Picks to perform the whole sequence of operations?

Input

The first line of input contains two integer: n, m (1 ≤ n, m ≤ 105). The second line contains n integers, separated by space: a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 109) — initial value of array elements.

Each of the next m lines begins with a number type <image>. 

  * If type = 1, there will be two integers more in the line: l, r (1 ≤ l ≤ r ≤ n), which correspond the operation 1. 
  * If type = 2, there will be three integers more in the line: l, r, x (1 ≤ l ≤ r ≤ n; 1 ≤ x ≤ 109), which correspond the operation 2. 
  * If type = 3, there will be two integers more in the line: k, x (1 ≤ k ≤ n; 1 ≤ x ≤ 109), which correspond the operation 3. 

Output

For each operation 1, please print a line containing the answer. Notice that the answer may exceed the 32-bit integer.

Examples

Input

5 5
1 2 3 4 5
2 3 5 4
3 3 5
1 2 5
2 1 3 3
1 1 3


Output

8
5


Input

10 10
6 9 6 7 6 1 10 10 9 5
1 3 9
2 7 10 9
2 5 10 8
1 4 7
3 3 7
2 7 9 9
1 2 4
1 6 6
1 5 9
3 1 10


Output

49
15
23
1
9

Note

Consider the first testcase:

  * At first, a = {1, 2, 3, 4, 5}. 
  * After operation 1, a = {1, 2, 3, 0, 1}. 
  * After operation 2, a = {1, 2, 5, 0, 1}. 
  * At operation 3, 2 + 5 + 0 + 1 = 8. 
  * After operation 4, a = {1, 2, 2, 0, 1}. 
  * At operation 5, 1 + 2 + 2 = 5. 

Example input:
5 5
1 2 3 4 5
2 3 5 4
3 3 5
1 2 5
2 1 3 3
1 1 3

10 10
6 9 6 7 6 1 10 10 9 5
1 3 9
2 7 10 9
2 5 10 8
1 4 7
3 3 7
2 7 9 9
1 2 4
1 6 6
1 5 9
3 1 10


Example output:
8
5

49
15
23
1
9


Tags: data structures
math
Difficulty rating: 2300

Solution:
#include <bits/stdc++.h>
using namespace std;
struct Lt {
  int x;
  long long s;
} Q[400000 + 3];
int n, m, Now, Lx, Rx;
void Edit(int w, int l, int r, int x) {
  if (l == r) {
    Q[w].x = Q[w].s = Now;
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    Edit(w << 1, l, mid, x);
  else
    Edit(w << 1 | 1, mid + 1, r, x);
  Q[w].x = max(Q[w << 1].x, Q[w << 1 | 1].x);
  Q[w].s = Q[w << 1].s + Q[w << 1 | 1].s;
}
long long Get(int w, int l, int r) {
  if (r < Lx || l > Rx) return 0;
  if (Lx <= l && r <= Rx) return Q[w].s;
  int mid = (l + r) >> 1;
  return Get(w << 1, l, mid) + Get(w << 1 | 1, mid + 1, r);
}
void Mod(int w, int l, int r) {
  if (r < Lx || l > Rx) return;
  if (Q[w].x < Now) return;
  if (l == r) {
    Q[w].x %= Now, Q[w].s = Q[w].x;
    return;
  }
  int mid = (l + r) >> 1;
  Mod(w << 1, l, mid);
  Mod(w << 1 | 1, mid + 1, r);
  Q[w].x = max(Q[w << 1].x, Q[w << 1 | 1].x);
  Q[w].s = Q[w << 1].s + Q[w << 1 | 1].s;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &Now), Edit(1, 1, n, i);
  }
  for (int i = 1; i <= m; i++) {
    int ty;
    scanf("%d", &ty);
    if (ty == 1) {
      scanf("%d%d", &Lx, &Rx);
      printf("%I64d\n", Get(1, 1, n));
    }
    if (ty == 2) {
      scanf("%d%d%d", &Lx, &Rx, &Now);
      Mod(1, 1, n);
    }
    if (ty == 3) {
      int x;
      scanf("%d%d", &x, &Now);
      Edit(1, 1, n, x);
    }
  }
}