Problem: 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. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int mx = 2e5 + 10;
using namespace std;
long long a[mx], seg[4 * mx], fen[mx], n, q;
void addf(int id, int val) {
  for (; id < mx && id != 0; id += id & -id) fen[id] += val;
}
long long getf(int id) {
  long long ans = 0;
  for (; id > 0; id -= id & -id) ans += fen[id];
  return ans;
}
void updateMAX(int p, int val, int l = 1, int r = n + 1, int id = 1) {
  if (r - l < 2) {
    seg[id] = val;
    return;
  }
  int mid = (l + r) >> 1;
  if (p < mid)
    updateMAX(p, val, l, mid, id << 1);
  else
    updateMAX(p, val, mid, r, id << 1 | 1);
  seg[id] = max(seg[id << 1], seg[id << 1 | 1]);
}
void updateMOD(int lq, int rq, int md, int l = 1, int r = n + 1, int id = 1) {
  if (rq <= l || r <= lq) return;
  if (r - l < 2) {
    addf(l, (a[l] % md) - a[l]);
    a[l] %= md;
    seg[id] = a[l];
    return;
  }
  int mid = (l + r) >> 1;
  if (seg[id << 1] >= md) updateMOD(lq, rq, md, l, mid, id << 1);
  if (seg[id << 1 | 1] >= md) updateMOD(lq, rq, md, mid, r, id << 1 | 1);
  seg[id] = max(seg[id << 1], seg[id << 1 | 1]);
}
int main() {
  scanf("%I64d%I46d", &n, &q);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]), addf(i, a[i]);
    updateMAX(i, a[i]);
  }
  while (q--) {
    int t, l, r, x;
    cin >> t;
    if (t == 1) {
      scanf("%d%d", &l, &r);
      printf("%I64d\n", getf(r) - getf(l - 1));
    } else if (t == 2) {
      scanf("%d%d%d", &l, &r, &x);
      updateMOD(l, r + 1, x);
    } else {
      int p, x;
      scanf("%d%d", &p, &x);
      updateMAX(p, x);
      addf(p, x - a[p]);
      a[p] = x;
    }
  }
}