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>
template <class T>
inline void read(T &x) {
  x = 0;
  T flag = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') flag *= -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = (x << 1) + (x << 3) + c - 48;
    c = getchar();
  }
  x *= flag;
}
struct Node {
  long long max, sum;
} tr[100007 << 2];
int n, m, a[100007], p;
inline long long max(long long x, long long y) { return x > y ? x : y; }
inline void update(int id) {
  tr[id].sum = tr[id << 1].sum + tr[id << 1 | 1].sum;
  tr[id].max = max(tr[id << 1].max, tr[id << 1 | 1].max);
}
void build(int id, int lf, int rf) {
  if (lf == rf)
    tr[id].max = tr[id].sum = a[lf];
  else {
    int mid = (lf + rf) >> 1;
    build(id << 1, lf, mid);
    build(id << 1 | 1, mid + 1, rf);
    update(id);
  }
}
int l, r, val;
void modify(int id, int lf, int rf) {
  if (lf == rf)
    tr[id].max = tr[id].sum = val;
  else {
    int mid = (lf + rf) >> 1;
    if (l <= mid)
      modify(id << 1, lf, mid);
    else
      modify(id << 1 | 1, mid + 1, rf);
    update(id);
  }
}
void Mod(int id, int lf, int rf) {
  if (tr[id].max < p) return;
  if (lf == rf) {
    tr[id].max %= p;
    tr[id].sum %= p;
  } else {
    int mid = (lf + rf) >> 1;
    if (l <= mid) Mod(id << 1, lf, mid);
    if (r > mid) Mod(id << 1 | 1, mid + 1, rf);
    update(id);
  }
}
long long query(int id, int lf, int rf) {
  if (l <= lf && rf <= r)
    return tr[id].sum;
  else {
    int mid = (lf + rf) >> 1;
    long long ret = 0;
    if (l <= mid) ret += query(id << 1, lf, mid);
    if (r > mid) ret += query(id << 1 | 1, mid + 1, rf);
    return ret;
  }
}
int main() {
  read(n), read(m);
  for (int i = 1; i <= n; i++) read(a[i]);
  build(1, 1, n);
  int opt;
  while (m--) {
    read(opt);
    if (opt == 1) {
      read(l), read(r);
      printf("%lld\n", query(1, 1, n));
    } else if (opt == 2) {
      read(l), read(r), read(p);
      Mod(1, 1, n);
    } else {
      read(l), read(val);
      modify(1, 1, n);
    }
  }
}