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>
using namespace std;
int a[100005];
pair<long long, int> st[400005];
pair<long long, int> merge(pair<long long, int> p1, pair<long long, int> p2) {
  if (a[p1.second] >= a[p2.second])
    return pair<long long, int>(p1.first + p2.first, p1.second);
  return pair<long long, int>(p1.first + p2.first, p2.second);
}
void update(int n, int s, int e, int idx) {
  if (s == e)
    st[n] = pair<long long, int>(a[idx], idx);
  else {
    int mid = (s + e) / 2;
    if (idx <= mid)
      update(n + n, s, mid, idx);
    else
      update(n + n + 1, mid + 1, e, idx);
    st[n] = merge(st[n + n], st[n + n + 1]);
  }
}
pair<long long, int> query(int n, int s, int e, int l, int r) {
  if (s > r || l > e) return pair<long long, int>(0, 0);
  if (l <= s && e <= r) return st[n];
  int mid = (s + e) / 2;
  return merge(query(n + n, s, mid, l, r), query(n + n + 1, mid + 1, e, l, r));
}
int main() {
  int n, m, t;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    update(1, 1, n, i);
  }
  for (int i = 1; i <= m; i++) {
    scanf("%d", &t);
    if (t == 1) {
      int l, r;
      scanf("%d%d", &l, &r);
      printf("%lld\n", query(1, 1, n, l, r).first);
    } else if (t == 2) {
      int l, r, x;
      scanf("%d%d%d", &l, &r, &x);
      while (1) {
        int idx = query(1, 1, n, l, r).second;
        if (a[idx] < x) break;
        a[idx] %= x;
        update(1, 1, n, idx);
      }
    } else {
      int k, x;
      scanf("%d%d", &k, &x);
      a[k] = x;
      update(1, 1, n, k);
    }
  }
}