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 static java.lang.Math.*;
import java.util.*;
import java.lang.*;

public class Main {
    final static boolean debug = false;
    final static String fileName = "";
    final static boolean useFiles = false;

    public static void main(String[] args) throws FileNotFoundException {
        long start;
        if (debug)
            start = System.nanoTime();
        InputStream inputStream;
        OutputStream outputStream;
        if (useFiles) {
            inputStream = new FileInputStream(fileName + ".in");
            outputStream = new FileOutputStream(fileName + ".out");
        } else {
            inputStream = System.in;
            outputStream = System.out;
        }
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task(in, out);
        solver.solve();
        if(debug)
            out.println((System.nanoTime() - start) / 1e+9);
        out.close();
    }
}

class Item {
    Item(long sum, int max, int index) {
        Sum = sum;
        Max = max;
        Index = index;
    }

    int Max, Index;
    long Sum;

    static Item combine(Item a, Item b) {
        if (a == null)
            return b;
        if (b == null)
            return a;
        return new Item(a.Sum + b.Sum, max(a.Max, b.Max), a.Max > b.Max ? a.Index : b.Index);
    }
}

class SegmentTree {
    private Item[] t;
    private int n;

    SegmentTree(int n) {
        this.n = n;
        t = new Item[n << 2];
    }

    SegmentTree(Item[] array) {
        this(array.length);
        build(0, 0, n - 1, array);
    }

    private void build(int v, int tl, int tr, Item[] array) {
        if (tr == tl) {
            t[v] = array[tl];
        } else {
            int tm = (tl + tr) >> 1;
            build(2 * v + 1, tl, tm, array);
            build(2 * v + 2, tm + 1, tr, array);
            t[v] = Item.combine(t[2 * v + 1], t[2 * v + 2]);
        }
    }

    Item get(int l, int r) {
        if (l >= n || r >= n || 0 > l || 0 > r)
            throw new IllegalArgumentException("indices: (" + l + ", " + r + "). Bounds: (0, "+ (n - 1) + ")");
        return get(0, 0, n - 1, l, r);
    }

    void assign(int index, Item value) {
        if (0 > index || index > n)
            throw new IllegalArgumentException("index: " + index + ". Bounds: " + (n - 1));
        assign(0, 0, n - 1, index, value);
    }

    private Item get(int v, int tl, int tr, int l, int r) {
        if (l > r)
            return null;
        if (tl == l && tr == r)
            return t[v];
        int tm = (tl + tr) >> 1;
        return Item.combine(get(2 * v + 1, tl, tm, l, Math.min(tm, r)),
                get(2 * v + 2, tm + 1, tr, Math.max(tm + 1, l), r));
    }

    private void assign(int v, int tl, int tr, int index, Item value) {
        if (tr == tl)
            t[v] = value;
        else {
            int tm = (tl + tr) >> 1;
            if (index <= tm)
                assign(2 * v + 1, tl, tm, index, value);
            else
                assign(2 * v + 2, tm + 1, tr, index, value);
            t[v] = Item.combine(t[2 * v + 1], t[2 * v + 2]);
        }
    }
}

class Task {
    public void solve() {
        int n = in.nextInt();
        int m = in.nextInt();
        Item[] a = new Item[n];
        for (int i = 0; i < n; i++) {
            int x = in.nextInt();
            a[i] = new Item(x, x, i);
        }
        SegmentTree tree = new SegmentTree(a);
        for (int i = 0; i < m; i++) {
            int type = in.nextInt();
            if (type == 1) {
                int l = in.nextInt() - 1;
                int r = in.nextInt() - 1;
                out.println(tree.get(l, r).Sum);
            } else if (type == 2) {
                int l = in.nextInt() - 1;
                int r = in.nextInt() - 1;
                int x = in.nextInt();
                for (; ; ) {
                    Item item = tree.get(l, r);
                    if (item.Max < x)
                        break;
                    tree.assign(item.Index, new Item(item.Max % x, item.Max % x, item.Index));
                }
            } else {
                int k = in.nextInt() - 1;
                int x = in.nextInt();
                tree.assign(k, new Item(x, x, k));
            }
        }
    }

    private InputReader in;
    private PrintWriter out;

    Task(InputReader in, PrintWriter out) {
        this.in = in;
        this.out = out;
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 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 double nextDouble(){
        return Double.parseDouble(next());
    }

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

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

    public byte nextByte(){
        return Byte.parseByte(next());
    }
}