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:
//package round250;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), Q = ni();
		int[] a = na(n);
		for(int i = 0;i < n;i++){
			a[i] = -a[i];
		}
		SegmentTreeRMQPos st = new SegmentTreeRMQPos(a);
		
		long[] b = new long[n];
		for(int i = 0;i < n;i++)b[i] = -a[i];
		long[] ft = buildFenwick(b);
		for(int z = 0;z < Q;z++){
			int t = ni();
			if(t == 1){
				int l = ni()-1, r = ni()-1;
				out.println(sumFenwick(ft, r) - sumFenwick(ft, l-1));
			}else if(t == 2){
				int l = ni()-1, r = ni()-1, x = ni();
				while(true){
					int[] mp = st.min(l, r);
					if(mp[0] > -x)break;
					st.update(mp[1], mp[0]%x);
					int plus = mp[0]/x*x;
					addFenwick(ft, mp[1], plus);
					b[mp[1]] %= x;
				}
			}else if(t == 3){
				int pos = ni()-1, x = ni();
				addFenwick(ft, pos, x-b[pos]);
				b[pos] = x;
				st.update(pos, -x);
			}
		}
	}
	
	public static long sumFenwick(long[] ft, int i)
	{
		long sum = 0;
		for(i++;i > 0;i -= i&-i)sum += ft[i];
		return sum;
	}
	
	public static void addFenwick(long[] ft, int i, long v)
	{
		if(v == 0)return;
		int n = ft.length;
		for(i++;i < n;i += i&-i)ft[i] += v;
	}
	
	public static int findGFenwick(long[] ft, long v)
	{
		int i = 0;
		int n = ft.length;
		for(int b = Integer.highestOneBit(n);b != 0 && i < n;b >>= 1){
			if(i + b < n){
				int t = i + b;
				if(v >= ft[t]){
					i = t;
					v -= ft[t];
				}
			}
		}
		return v != 0 ? -(i+1) : i-1;
	}
	
	public static long[] restoreFenwick(long[] ft)
	{
		int n = ft.length-1;
		long[] ret = new long[n];
		for(int i = 0;i < n;i++)ret[i] = sumFenwick(ft, i);
		for(int i = n-1;i >= 1;i--)ret[i] -= ret[i-1];
		return ret;
	}
	
	public static long[] buildFenwick(long[] a)
	{
		int n = a.length;
		long[] ft = new long[n+1];
		System.arraycopy(a, 0, ft, 1, n);
		for(int k = 2, h = 1;k <= n;k*=2, h*=2){
			for(int i = k;i <= n;i+=k){
				ft[i] += ft[i-h];
			}
		}
		return ft;
	}
	
	public static class SegmentTreeRMQPos {
		public int M, H, N, B;
		public int[] st;
		public int[] pos;
		
		public SegmentTreeRMQPos(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n, 1))<<2;
			H = M>>>1;
			B = Integer.numberOfTrailingZeros(H);
			st = new int[M];
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 0;i--){
				pos[i] = pos[2*i];
			}
		}
		
		public SegmentTreeRMQPos(int[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N, 1))<<2;
			H = M>>>1;
			B = Integer.numberOfTrailingZeros(H);
			st = new int[M];
			pos = new int[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
				pos[H+i] = i;
			}
			Arrays.fill(st, H+N, M, Integer.MAX_VALUE);
			for(int i = (M>>1)-1;i >= 1;i--)propagate(i);
		}
		
		public void update(int p, int x)
		{
			st[H+p] = x;
			for(int i = (H+p)>>>1;i >= 1;i >>>= 1)propagate(i);
		}
		
		private void propagate(int i)
		{
			if(st[i*2] <= st[i*2+1]){
				st[i] = st[i*2];
				pos[i] = pos[i*2];
			}else{
				st[i] = st[i*2+1];
				pos[i] = pos[i*2+1];
			}
		}
		
		public int[] min(int f, int t) { return min(f, t, B); }
		
		public int[] min(int f, int t, int b)
		{
			if(f>>b<<b==f && t+1>>b<<b==t+1){
				return new int[]{st[(H|f)>>b], pos[(H|f)>>b]};
			}
			
			b--;
			if((f^t)<<31-b<0){
				int w = t>>b<<b;
				int[] l = min(f, w-1, b);
				int[] r = min(w, t, b);
				return l[0] <= r[0] ? l : r;
			}else{
				return min(f, t, b);
			}
		}
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}