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.*;
import java.math.*;
import java.util.*;

public class Main {
    int getLocation(int l, int r) {
        return l + r | (l != r ? 1 : 0);
    }

    long[] sum;
    Pair[] max;

    long getSum(int l, int r, int a, int b) {
        if (b < l || r < a) {
            return 0;
        }
        int id = getLocation(l, r);
        if (a <= l && r <= b) {
            return sum[id];
        }
        int m = l + r >> 1;
        return getSum(l, m, a, b) + getSum(m + 1, r, a, b);
    }

    Pair getMax(int l, int r, int a, int b) {
        if (b < l || r < a) {
            return new Pair(-1, -1);
        }
        int id = getLocation(l, r);
        if (a <= l && r <= b) {
            return max[id];
        }
        int m = l + r >> 1;
        return myMax(getMax(l, m, a, b), getMax(m + 1, r, a, b));
    }

    void modify(int l, int r, int k, int v) {
        if (k < l || r < k) {
            return;
        }
        int id = getLocation(l, r);
        if (l == r) {
            sum[id] = v;
            max[id] = new Pair(v, l);
        } else {
            int m = l + r >> 1;
            modify(l, m, k, v);
            modify(m + 1, r, k, v);
            sum[id] = sum[getLocation(l, m)] + sum[getLocation(m + 1, r)];
            max[id] = myMax(max[getLocation(l, m)], max[getLocation(m + 1, r)]);
        }
    }

    public void run() {
        try {
            int n = reader.nextInt();
            int m = reader.nextInt();
            sum = new long[n << 1];
            max = new Pair[n << 1];
            Arrays.fill(max, new Pair(-1, -1));
            int[] a = new int[n];
            for (int i = 0; i < n; ++ i) {
                a[i] = reader.nextInt();
                modify(0, n - 1, i, a[i]);
            }
            while (m > 0) {
                m --;
                int t = reader.nextInt();
                if (t == 1) {
                    int l = reader.nextInt() - 1;
                    int r = reader.nextInt() - 1;
                    writer.println(getSum(0, n - 1, l, r));
                } else if (t == 2) {
                    int l = reader.nextInt() - 1;
                    int r = reader.nextInt() - 1;
                    int x = reader.nextInt();
                    while (true) {
                        Pair mp = getMax(0, n - 1, l, r);
                        if (mp.max < x) {
                            break;
                        }
                        int i = mp.index;
                        modify(0, n - 1, i, mp.max % x);
                    }
                } else if (t == 3) {
                    int k = reader.nextInt() - 1;
                    int x = reader.nextInt();
                    modify(0, n - 1, k, x);
                } else {
                    assert false;
                }
            }
        } catch (IOException ex) {
        }
        writer.close();
    }

    Pair myMax(Pair a, Pair b) {
        return a.compareTo(b) > 0 ? a : b;
    }

    class Pair implements Comparable {
        Pair(int max, int index) {
            this.max   = max;
            this.index = index;
        }

        @Override
        public int compareTo(Object other) {
            return max - ((Pair)other).max;
        }

        int max, index;
    }

    Main() {
        reader = new InputReader(System.in);
        writer = new PrintWriter(System.out);
    }

    public static void main(String[] args) {
        new Main().run();
    }

    private void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    private InputReader reader;
    private PrintWriter writer;
}

class InputReader {
    InputReader(InputStream in) {
        reader    = new BufferedReader(new InputStreamReader(in));
        tokenizer = new StringTokenizer("");
    }

    private String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

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

    private BufferedReader  reader;
    private StringTokenizer tokenizer;
}