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;
template <typename TI, typename TX>
class SegmentTree {
 public:
  struct node {
    TI x;
    int mx = -1e9;
    int id = -1;
    node() { x = 0; };
    node(const TX &y, int id) { set(y, id); };
    void set(const TX &y, int id1) {
      x = y;
      id = id1;
      mx = y;
    };
  };
  node merge(const node &a, const node &b) {
    node ans = a;
    ans.x = a.x + b.x;
    if (b.mx > a.mx) {
      ans.mx = b.mx;
      ans.id = b.id;
    }
    return ans;
  }
  int n;
  vector<node> tree;
  inline void unite(int v, int a, int b) { tree[v] = merge(tree[a], tree[b]); }
  void build(int v, int l, int r, const vector<TX> &A) {
    if (l == r) {
      tree[v].set(A[l], l);
      return;
    }
    int left = v << 1, right = v << 1 | 1;
    int md = (l + r) >> 1;
    build(left, l, md, A);
    build(right, md + 1, r, A);
    unite(v, left, right);
  }
  void build(int v, int l, int r) {
    if (l == r) {
      return;
    }
    int left = v << 1, right = v << 1 | 1;
    int md = (l + r) >> 1;
    build(left, l, md);
    build(right, md + 1, r);
    unite(v, left, right);
  }
  SegmentTree(int _n) : n(_n) {
    assert(n > 0);
    tree.resize(4 * n);
    build(1, 0, n - 1);
  }
  SegmentTree(const vector<TX> &A) {
    n = A.size();
    assert(n > 0);
    tree.resize(4 * n);
    build(1, 0, n - 1, A);
  }
  node get(int v, int l, int r, int ll, int rr) {
    if (l > r) {
      return node();
    }
    if (l == ll && r == rr) {
      return tree[v];
    }
    int left = v << 1, right = v << 1 | 1;
    int md = (ll + rr) >> 1;
    node a = get(left, l, min(md, r), ll, md);
    node b = get(right, max(md + 1, l), r, md + 1, rr);
    return merge(a, b);
  }
  template <typename T>
  void update(int v, int ll, int rr, int p, const T &x) {
    if (ll == rr) {
      tree[v].set(x, p);
      return;
    }
    int left = v << 1, right = v << 1 | 1;
    int md = (ll + rr) >> 1;
    if (p <= md) {
      update(left, ll, md, p, x);
    } else {
      update(right, md + 1, rr, p, x);
    }
    unite(v, left, right);
  }
  node get(int i) {
    assert(i >= 0 && i < n);
    node ans = get(1, i, i, 0, n - 1);
    return ans;
  }
  node get(int l, int r) {
    assert(l <= r);
    assert(l >= 0 && r < n);
    node ans = get(1, l, r, 0, n - 1);
    return ans;
  }
  template <typename T>
  void update(int p, const T &x) {
    assert(p >= 0 && p < n);
    update(1, 0, n - 1, p, x);
  }
};
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<int> A(n);
  for (int i = 0; i < n; i++) {
    cin >> A[i];
  }
  SegmentTree<long long, int> sg(A);
  int l, r, x;
  while (m--) {
    int ty;
    cin >> ty;
    if (ty == 1) {
      cin >> l >> r;
      l--, r--;
      cout << sg.get(l, r).x << '\n';
    } else if (ty == 2) {
      cin >> l >> r;
      l--, r--;
      cin >> x;
      int h = 0;
      do {
        auto nd = sg.get(l, r);
        h = nd.mx;
        if (h >= x) {
          sg.update(nd.id, h % x);
        } else
          break;
      } while (1);
    } else {
      cin >> l >> x;
      l--;
      sg.update(l, x);
    }
  }
  return 0;
}