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.util.*;

public class Main {
    static final long MOD = 1000000007;
    static int n, m;
    static int[] a;
    static Segment[] segments;
    
    static void init() {
        segments = new Segment[n * 4 + 10];
        build(0, 0, n - 1);
    }
    
    static void build(int index, int left, int right) {
        segments[index] = new Segment(left, right);
        if (left == right) {
            segments[index].max = a[left];
            segments[index].sum = a[left];
        } else {
            int mid = left + (right - left) / 2;
            build(index * 2 + 1, left, mid);
            build(index * 2 + 2, mid + 1, right);
            segments[index].max = Math.max(segments[index * 2 + 1].max,
                    segments[index * 2 + 2].max);
            segments[index].sum = segments[index * 2 + 1].sum + 
                    segments[index * 2 + 2].sum;
        }
    }
    
    static long get(int index, int left, int right) {
        if (segments[index].left == left && segments[index].right == right) {
            return segments[index].sum;
        } else {
            int mid = segments[index].left + (segments[index].right - segments[index].left) /  2;
            if (mid >= right) {
                return get(index * 2 + 1, left, right);
            } else if (mid < left) {
                return get(index * 2 + 2, left, right);
            } else {
                return get(index * 2 + 1, left, mid) + 
                        get(index * 2 + 2, mid + 1, right);
            }
        }
    }
    
    static void mod(int index, int left, int right, int x) {
        if (segments[index].max < x) {
            return;
        }
        
        int len = segments[index].right - segments[index].left;
        if (len == 0) {
            segments[index].sum = segments[index].max = a[left] = (a[left] % x);
        } else {
            int mid = segments[index].left + len / 2;
            if (mid >= right) {
                mod(index * 2 + 1, left, right, x);
            } else if (mid < left) {
                mod(index * 2 + 2, left, right, x);
            } else {
                mod(index * 2 + 1, left, mid, x);
                mod(index * 2 + 2, mid + 1, right, x);
            }

            segments[index].max = Math.max(segments[index * 2 + 1].max,
                    segments[index * 2 + 2].max);
            segments[index].sum = segments[index * 2 + 1].sum + 
                    segments[index * 2 + 2].sum;
        }
    }
    
    static void set(int index, int pos, int x) {
        int len = segments[index].right - segments[index].left;
        if (len == 0) {
            segments[index].sum = segments[index].max = a[pos] = x;
        } else {
            int mid = segments[index].left + len / 2;
            if (mid >= pos) {
                set(index * 2 + 1, pos, x);
            } else {
                set(index * 2 + 2, pos, x);
            }
            segments[index].max = Math.max(segments[index * 2 + 1].max,
                    segments[index * 2 + 2].max);
            segments[index].sum = segments[index * 2 + 1].sum + 
                    segments[index * 2 + 2].sum;
        }
    }
    
    public static void main(String[] args) throws Exception {
        FastScanner scan = new FastScanner(System.in);
        n = scan.nextInt();
        m = scan.nextInt();
        a = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = scan.nextInt();
        }
        int[][] order = new int[m][4];
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < 3; ++j) {
                order[i][j] = scan.nextInt();
            }
            if (order[i][0] == 2) {
                order[i][3] = scan.nextInt();
            }
        }
        
        init();
        
        StringBuilder builder = new StringBuilder(m * 10);
        for (int i = 0; i < m; ++i) {
            if (order[i][0] == 1) {
                builder.append(Long.toString(get(0, order[i][1] - 1, order[i][2] - 1)));
                builder.append('\n');
            } else if (order[i][0] == 2) {
                mod(0, order[i][1] - 1, order[i][2] - 1, order[i][3]);
            } else {
                int pos = order[i][1] - 1;
                int x = order[i][2];
                if (a[pos] != x) {
                    set(0, pos, x);
                }
            }
        }
        System.out.print(builder.toString());
        System.out.flush();
    }
}

class FastScanner {
    BufferedReader in;
    StringTokenizer tok;

    public FastScanner(InputStream in) {
        this.in = new BufferedReader(new InputStreamReader(in));
        tok = new StringTokenizer("");
    }

    private String tryReadNextLine() {
        try {
            return in.readLine();
        } catch (Exception e) {
            throw new InputMismatchException();
        }
    }

    public String nextToken() {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(next());
        }
        return tok.nextToken();
    }

    private String next() {
        String newLine = tryReadNextLine();
        if (newLine == null)
            throw new InputMismatchException();
        return newLine;
    }

    public int nextInt() {
        return Integer.parseInt(nextToken());
    }
    
    public double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() {
        return Long.parseLong(nextToken());
    }

}


class Segment {
    public int left;
    public int right;
    public int max;
    public long sum;
    public boolean changed;
    public Segment(int left, int right) {
        this.left = left;
        this.right = right;
    }
    public String toString() {
        return String.format("(%d,%d)", left, right);
    }
}