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;
const int maxn = 112345;
struct Seg {
  int l, r;
  int p, mx;
  long long sum;
} T[maxn << 2];
int n, m;
int a[maxn];
void push_up(int o) {
  T[o].sum = T[o << 1].sum + T[o << 1 | 1].sum;
  if (T[o << 1].mx > T[o << 1 | 1].mx) {
    T[o].mx = T[o << 1].mx;
    T[o].p = T[o << 1].p;
  } else {
    T[o].mx = T[o << 1 | 1].mx;
    T[o].p = T[o << 1 | 1].p;
  }
}
void build(int o, int l, int r) {
  T[o].l = l, T[o].r = r;
  if (l == r) {
    T[o].sum = T[o].mx = a[l];
    T[o].p = l;
  } else {
    int mi = l + r >> 1;
    build(o << 1, l, mi);
    build(o << 1 | 1, mi + 1, r);
    push_up(o);
  }
}
long long query(int o, int l, int r) {
  if (l <= T[o].l && T[o].r <= r) return T[o].sum;
  long long ret = 0;
  int mi = T[o].l + T[o].r >> 1;
  if (l <= mi) ret += query(o << 1, l, r);
  if (r > mi) ret += query(o << 1 | 1, l, r);
  return ret;
}
pair<int, int> get_mx(int o, int l, int r) {
  if (l <= T[o].l && T[o].r <= r) return {T[o].mx, T[o].p};
  pair<int, int> ret = {0, 0};
  int mi = T[o].l + T[o].r >> 1;
  if (l <= mi) ret = max(ret, get_mx(o << 1, l, r));
  if (r > mi) ret = max(ret, get_mx(o << 1 | 1, l, r));
  return ret;
}
void update(int o, int p, int x) {
  if (T[o].l == T[o].r) {
    T[o].sum = T[o].mx = x;
    return;
  }
  int mi = T[o].l + T[o].r >> 1;
  if (p <= mi)
    update(o << 1, p, x);
  else
    update(o << 1 | 1, p, x);
  push_up(o);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m;
  for (int(i) = (1); (i) <= (n); (i)++) cin >> a[i];
  build(1, 1, n);
  while (m--) {
    int type;
    cin >> type;
    if (type == 1) {
      int l, r;
      cin >> l >> r;
      cout << query(1, l, r) << '\n';
    } else if (type == 2) {
      int l, r, x;
      cin >> l >> r >> x;
      while (true) {
        auto [v, p] = get_mx(1, l, r);
        if (v < x) break;
        update(1, p, v % x);
      }
    } else {
      int k, x;
      cin >> k >> x;
      update(1, k, x);
    }
  }
}