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;
void debug_out() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << H;
  debug_out(T...);
}
const long long MAXN = 1e5 + 10;
long long n, m, a, l, r, x, k, type, seg[2][MAXN << 2];
void SET(long long p, long long x, long long id = 1, long long second = 0,
         long long e = n) {
  if (e - second < 2) {
    seg[0][id] = seg[1][id] = x;
    return;
  }
  long long mid = (second + e) >> 1;
  if (p < mid)
    SET(p, x, id << 1, second, mid);
  else
    SET(p, x, id << 1 | 1, mid, e);
  seg[0][id] = seg[0][id << 1] + seg[0][id << 1 | 1],
  seg[1][id] = max(seg[1][id << 1], seg[1][id << 1 | 1]);
  return;
}
void update(long long l, long long r, long long x, long long id = 1,
            long long second = 0, long long e = n) {
  if (e <= l or r <= second or seg[1][id] < x) return;
  if (e - second < 2) {
    seg[0][id] %= x, seg[1][id] %= x;
    return;
  }
  long long mid = (second + e) >> 1;
  update(l, r, x, id << 1, second, mid), update(l, r, x, id << 1 | 1, mid, e);
  seg[0][id] = seg[0][id << 1] + seg[0][id << 1 | 1],
  seg[1][id] = max(seg[1][id << 1], seg[1][id << 1 | 1]);
  return;
}
long long get(long long l, long long r, long long id = 1, long long second = 0,
              long long e = n) {
  if (e <= l or r <= second) return 0;
  if (l <= second and e <= r) return seg[0][id];
  long long mid = (second + e) >> 1,
            left_child = get(l, r, id << 1, second, mid),
            right_child = get(l, r, id << 1 | 1, mid, e);
  return left_child + right_child;
}
int32_t main() {
  cin >> n >> m;
  for (long long i = 0; i < n; i++) cin >> a, SET(i, a);
  while (m--) {
    cin >> type, type--;
    if (!type)
      cin >> l >> r, l--, cout << get(l, r) << '\n';
    else if (--type)
      cin >> k >> x, k--, SET(k, x);
    else
      cin >> l >> r >> x, l--, update(l, r, x);
  }
  return 0;
}