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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution {
    private static class SumSegmentTree {
        final int size;
        final long[] tree;

        private SumSegmentTree(int size) {
            int q = 1;
            while (q <= size) {
                q *= 2;
            }
            this.size = q;
            this.tree = new long[2 * q];
        }

        void set(int i, long x) {
            tree[i + size] = x;
            for (int k = (i + size) / 2; k > 0; k /= 2) {
                tree[k] = tree[2 * k] + tree[2 * k + 1];
            }
        }

        long getValue(int l, int r) {
            long value = 0;
            for (l += size, r += size; l < r; l /= 2, r /=2 ) {
                if (l % 2 == 1) {
                    value += tree[l++];
                }
                if (r % 2 == 1) {
                    value += tree[--r];
                }
            }
            return value;
        }
    }

    private static class MaxSegmentTree {
        final int size;
        final int[] tree;
        final SumSegmentTree sumSegmentTree;

        private MaxSegmentTree(int size, SumSegmentTree sumSegmentTree) {
            this.sumSegmentTree = sumSegmentTree;
            int q = 1;
            while (q <= size) {
                q *= 2;
            }
            this.size = q;
            this.tree = new int[2 * q];
        }

        void set(int i, int x) {
            tree[i + size] = x;
            for (int k = (i + size) / 2; k > 0; k /= 2) {
                tree[k] = Math.max(tree[2 * k], tree[2 * k + 1]);
            }
        }

        long getValue(int l, int r) {
            long value = 0;
            for (l += size, r += size; l < r; l /= 2, r /=2 ) {
                if (l % 2 == 1) {
                    value = Math.max(value, tree[l++]);
                }
                if (r % 2 == 1) {
                    value = Math.max(value, tree[--r]);
                }
            }
            return value;
        }

        private void traverseAndUpdate(int l, int r,
                                       int node, int nodeL, int nodeR,
                                       int mod) {
            if (tree[node] < mod) {
                return;
            }
            if (nodeR - nodeL == 1) {
                int x = tree[node] % mod;
                tree[node] = x;
                sumSegmentTree.set(nodeL, x);
                return;
            }
            int middle = (nodeL + nodeR) / 2;
            if (l < middle) {
                traverseAndUpdate(l, Math.min(r, middle), 2 * node, nodeL, middle, mod);
            }
            if (r > middle) {
                traverseAndUpdate(Math.max(l, middle), r, 2 * node + 1, middle, nodeR, mod);
            }
            tree[node] = Math.max(tree[2 * node], tree[2 * node + 1]);
        }

        void traverseAndUpdate(int l, int r, int mod) {
            traverseAndUpdate(l, r, 1, 0, size, mod);
        }
    }

    public static void main(String[] args) throws IOException {
        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
             PrintWriter writer = new PrintWriter(System.out)) {
            int n = nextInt(reader);
            int q = nextInt(reader);
            SumSegmentTree sumTree = new SumSegmentTree(n);
            MaxSegmentTree maxTree = new MaxSegmentTree(n, sumTree);
            for (int i = 0; i < n; i++) {
                int x = nextInt(reader);
                sumTree.set(i, x);
                maxTree.set(i, x);
            }
            for (int k = 0; k < q; k++) {
                int type = nextInt(reader);
                if (type == 1) {
                    int from = nextInt(reader) - 1;
                    int to = nextInt(reader);
                    writer.println(sumTree.getValue(from, to));
                }
                if (type == 2) {
                    int from = nextInt(reader) - 1;
                    int to = nextInt(reader);
                    int mod = nextInt(reader);
                    maxTree.traverseAndUpdate(from, to, mod);
                }
                if (type == 3) {
                    int where = nextInt(reader) - 1;
                    int newValue = nextInt(reader);
                    sumTree.set(where, newValue);
                    maxTree.set(where, newValue);
                }
            }
        }
    }

    private static StringTokenizer stringTokenizer;

    private static String next(BufferedReader reader) throws IOException {
        if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

    private static int nextInt(BufferedReader reader) throws IOException {
        return Integer.parseInt(next(reader));
    }

    private static long nextLong(BufferedReader reader) throws IOException {
        return Long.parseLong(next(reader));
    }
}