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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class P438d {

  public static void main(String[] args) {
    InputReader in = new InputReader(System.in);
    PrintWriter out = new PrintWriter(System.out);

    Solver.solve(in, out);
  }

  static class Solver {

    static void solve(InputReader in, PrintWriter out) {
      int n = in.nextInt();
      int m = in.nextInt();
      int[] a = new int[n];
      for(int i = 0; i < n; i++) {
        a[i] = in.nextInt();
      }

      SegmentTree st = new SegmentTree(a);
      for(int i = 0; i < m; i++) {
        switch(in.nextInt()) {
          case 1:
            int l1 = in.nextInt();
            int r1 = in.nextInt();
            out.println(st.partialSum(l1 - 1, r1));
            break;
          case 2:
            int l2 = in.nextInt();
            int r2 = in.nextInt();
            int x2 = in.nextInt();
            st.applyModulus(l2 - 1, r2, x2);
            break;
          case 3:
            int k3 = in.nextInt();
            int x3 = in.nextInt();
            st.set(k3 - 1, x3);
            break;
        }
      }
      out.flush();
    }
  }

  static class SegmentTree {
    int[] max;
    long[] sum;
    int[] a;
    int n;

    public SegmentTree(int[] a) {
      this.a = a;
      this.n = a.length;
      this.max = new int[4 * n];
      this.sum = new long[4 * n];
      build(1, 0, n);
      int k = 1;
    }

    private void build(int id, int l, int r) {
      if(r == l + 1) {
        // leaf
        max[id] = a[l];
        sum[id] = a[l];
        return;
      }
      // not leaf
      int mid = (r + l) / 2;
      build(id * 2, l, mid);
      build(id * 2 + 1, mid, r);
      recalculateNodeFromChildren(id);
    }

    // sum of elements [x, y)
    public long partialSum(int x, int y) {
      return partialSum(1, 0, n, x, y);
    }

    // returns sum of elements [x, y) contained in node with given id
    // node id is for range [l, r).
    private long partialSum(int id, int l, int r, int x, int y) {
      if(x >= r || y <= l) {
        return 0;
      }
      if(x <= l && y >= r) {
        return sum[id];
      }
      int mid = (l + r) / 2;
      long leftSum = partialSum(id * 2, l, mid, x, y);
      long rightSum = partialSum(id * 2 + 1, mid, r, x, y);
      return leftSum + rightSum;
    }

    // Sets a[i] = val & updates ST
    public void set(int i, int val) {
      set(1, 0, n, i, val);
    }

    // Sets a[i] = val & updates ST
    private void set(int id, int l, int r, int i, int val) {
      if(i < l || i >= r) {
        // outside node
        return;
      }

      if(r == l + 1) {
        // leaf
        sum[id] = val;
        max[id] = val;
        a[i] = val;
      } else {
        // not leaf
        int mid = (r + l) / 2;
        set(id * 2, l, mid, i, val);
        set(id * 2 + 1, mid, r, i, val);
        recalculateNodeFromChildren(id);
      }
    }

    // sets a[x, y) %= val
    public void applyModulus(int x, int y, int val) {
      applyModulus(1, 0, n, x, y, val);
    }

    private void applyModulus(int id, int l, int r, int x, int y, int val) {
      if(y <= l || x >= r) {
        // outside range
        return;
      }

      // skip node & children since mod will have no effect
      if(val > max[id]) {
        return;
      }


      if(r == l + 1) {
        // leaf
        a[l] %= val;
        sum[id] = a[l];
        max[id] = a[l];
      } else {
        // non-leaf
        int mid = (l + r) / 2;
        applyModulus(id * 2, l, mid, x, y, val);
        applyModulus(id * 2 + 1, mid, r, x, y, val);
        recalculateNodeFromChildren(id);
      }
    }

    private void recalculateNodeFromChildren(int id) {
      sum[id] = sum[id * 2] + sum[id * 2 + 1];
      max[id] = Math.max(max[id * 2], max[id * 2 + 1]);
    }
  }

  static class InputReader {

    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream inStream) {
      reader = new BufferedReader(new InputStreamReader(inStream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}