Problem: Let D(x) be the number of positive divisors of a positive integer x. For example, D(2) = 2 (2 is divisible by 1 and 2), D(6) = 4 (6 is divisible by 1, 2, 3 and 6).

You are given an array a of n integers. You have to process two types of queries:

  1. REPLACE l r — for every <image> replace ai with D(ai); 
  2. SUM l r — calculate <image>. 



Print the answer for each SUM query.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 3·105) — the number of elements in the array and the number of queries to process, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the elements of the array.

Then m lines follow, each containing 3 integers ti, li, ri denoting i-th query. If ti = 1, then i-th query is REPLACE li ri, otherwise it's SUM li ri (1 ≤ ti ≤ 2, 1 ≤ li ≤ ri ≤ n).

There is at least one SUM query.

Output

For each SUM query print the answer to it.

Example

Input

7 6
6 4 1 10 3 2 4
2 1 7
2 4 5
1 3 5
2 4 4
1 5 7
2 1 7


Output

30
13
4
22

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;
public class ai {
    InputStream is;
    PrintWriter out;
    long mod = (long)(1e9 + 7), inf = (long)(3e18);
    int cnt[];
    void solve() throws IOException {
        int arr[]=sieve(1000005);
        HashMap<Long,Integer> map = new HashMap();
        map.put(1l,1);
        map.put(2l,2);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new
                FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        for(int i=3;i<1000005;i++){
            int n = i;
            int x = arr[n];
            int ans = 1;
            int j = n/x;
            int c = 1;
            while(j!=1){
                if(arr[j]==x)c++;
                else{
                    ans *= c+1;
                    c=1;
                    x = arr[j];
                }
                j/=arr[j];
            }
            ans *= c+1;
            map.put(1l*i,ans);
        }
        int n = ni();
        int q = ni();
        int a[]=new int[n];
        long brr[]=new long[4*n];
        long crr[]=new long[4*n];
        for(int i=0;i<n;i++)a[i]=ni();
        build(brr,crr,a,1,0,n-1);
        while(q>0){
            q--;
            int t = ni();
            if(t==2){
                int x = ni();
                int y = ni();
                out.write(""+sum(brr, 0, n - 1, 1, x - 1, y - 1)+"\n");
            }
            else{
                int x = ni();
                int y = ni();
                x--;
                y--;
                increment(brr,crr,1,x,y,0,n-1,map);
            }
        }
        out.flush();
    }
    public void build(long arr[],long brr[],int a[],int n,int l,int r){
        if(l==r){
            arr[n] = brr[n] = a[l];
        }
        else{
            int mid = (l+r)/2;
            build(arr,brr,a,2*n,l,mid);
            build(arr,brr,a,2*n+1,mid+1,r);
            arr[n] = arr[2*n] + arr[2*n+1];
            brr[n] = Math.max(brr[2*n],brr[2*n+1]);
        }
    }
    public long sum(long arr[],int l,int r,int n,int start,int end){
        if(start>end)return 0;
        if(l==start && r==end){
            return arr[n];
        }
        int mid = (l+r)/2;
        return sum(arr,l,mid,2*n,start,Math.min(end,mid)) + sum(arr,mid+1,r,2*n+1,Math.max(mid+1,start),end);
    }
    public void increment(long arr[],long brr[],int n,int l,int r,int tl,int tr,HashMap<Long,Integer> map){
        if(l>r)return;
        if(l==r && tl==tr){
            arr[n] = map.get(arr[n]);
            brr[n] = map.get(brr[n]);
        }
        else{
            int mid = (tl+tr)/2;
            if(brr[2*n]>2)
            increment(arr,brr,2*n,l,Math.min(r,mid),tl,mid,map);
            if(brr[2*n+1]>2)
            increment(arr,brr,2*n+1,Math.max(l,mid+1),r,mid+1,tr,map);
            arr[n] = arr[2*n] + arr[2*n+1];
            brr[n] = Math.max(brr[2*n],brr[2*n+1]);
        }
    }
    public int[] sieve(int n){
        int []ans = new int[n];
        ans[1]=1;
        int i=2;
        while(i<n){
            if(ans[i]==0){
                int j=2*i;
                ans[i]=i;
                while(j<n){
                    if(ans[j]==0)
                        ans[j] = i;
                    j+=i;
                }
            }
            i++;
        }
        return ans;
    }
    public static void main(String[] args)throws Exception { new ai().run(); }
    void run() throws Exception {
        is = System.in;
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    byte input[] = new byte[1024];
    int len = 0, ptr = 0;

    int readByte() {
        if(ptr >= len) { ptr = 0;
            try { len = is.read(input); }
            catch(IOException e) { throw new InputMismatchException(); }
            if(len <= 0) { return -1; }
        } return input[ptr++];
    }
    boolean isSpaceChar(int c) { return !( c >= 33 && c <= 126 ); }
    int skip() {
        int b = readByte();
        while(b != -1 && isSpaceChar(b)) { b = readByte(); }
        return b;
    }

    char nc() { return (char)skip(); }
    String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!isSpaceChar(b)) { sb.appendCodePoint(b); b = readByte(); }
        return sb.toString();
    }
    String nLine() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while( !(isSpaceChar(b) && b != ' ') ) { sb.appendCodePoint(b); b = readByte(); }
        return sb.toString();
    }
    int ni() {
        int n = 0, b = readByte();
        boolean minus = false;
        while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); }
        if(b == '-') { minus = true; b = readByte(); }
        if(b == -1) { return -1; }  //no input
        while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); }
        return minus ? -n : n;
    }
    long nl() {
        long n = 0L;    int b = readByte();
        boolean minus = false;
        while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')) { b = readByte(); }
        if(b == '-') { minus = true; b = readByte(); }
        while(b >= '0' && b <= '9') { n = n * 10 + (b - '0'); b = readByte(); }
        return minus ? -n : n;
    }

    double nd() { return Double.parseDouble(ns()); }
    float nf() { return Float.parseFloat(ns()); }
    int[] na(int n) {
        int a[] = new int[n];
        for(int i = 0; i < n; i++) { a[i] = ni(); }
        return a;
    }
    char[] ns(int n) {
        char c[] = new char[n];
        int i, b = skip();
        for(i = 0; i < n; i++) {
            if(isSpaceChar(b)) { break; }
            c[i] = (char)b; b = readByte();
        } return i == n ? c : Arrays.copyOf(c,i);
    }
}