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.util.*;
import java.io.*;

public class MainA
{

    static int mod = (int) (1e9 + 7);
    static InputReader in;
    static PrintWriter out;
    static int[] cnt;
    static int[] arr;
    
    static class SegmentTree {
        long st[];
        long max[];
 
        SegmentTree(int n)  {
            st = new long[4*n];
            max = new long[4*n];
            build(0, n - 1, 1);
        }
        
        int getMid(int s, int e) {
            return (s+e)>>1;
        }

        long merge(long a,long b){
            return a+b;
        }
        
        long merge2(long a,long b){
            if(a > b) return a;
            return b;
        }
        
        void update(int s, int e, int x, int y, int c, int si){
            if(max[si] <= 2) return;
            if(s == x && e == y){
                if(x == y){
                    st[si] = cnt[(int)st[si]];
                    max[si] = st[si];
                    return;
                }
                int mid = getMid(s, e);
                
                update(s, mid, x, mid, c, 2*si);
                update(mid + 1, e, mid + 1, y, c, 2*si + 1);
            }
            else{
                int mid = getMid(s, e);
                if(y <= mid)    
                    update(s, mid, x, y, c, 2*si);
                else if(x > mid)
                    update(mid + 1, e, x ,y ,c ,2*si + 1);
                else{
                    update(s, mid, x, mid, c, 2*si);
                    update(mid + 1, e, mid + 1, y, c, 2*si + 1);
                }
            }
            st[si] = merge(st[2*si],st[2*si+1]);
            max[si] = merge2(max[2*si],max[2*si+1]);
        }

        long  get(int s, int e, int x, int y, int si){

            if(s == x && e == y){
                return st[si];
            }
            int mid = getMid(s, e);
            if(y <= mid)
                return get(s, mid, x, y, 2*si);
            else if(x > mid)
                return get(mid + 1, e, x, y, 2*si + 1);
            return merge(get(s, mid, x, mid, 2*si), get(mid + 1, e, mid + 1, y, 2*si + 1));
        }

        void build(int ss, int se, int si){
            if (ss == se) {
                st[si] = arr[ss];
                max[si] = st[si];
                return;
            }

            int mid = getMid(ss, se);
            build(ss, mid, si * 2 );
            build(mid + 1, se, si * 2 + 1);
            st[si] = merge(st[2*si],st[2*si+1]);
            max[si] = merge2(max[2*si],max[2*si+1]);
        }
    }

        
    public static void main(String[] args)
    {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        int maxn = 1000001;
        cnt = new int[maxn];
        Arrays.fill(cnt, 1);

        for(int i = 2; i < maxn; i++)
            for(int j = i; j < maxn; j += i)
                cnt[j]++;
        
        int n = in.nextInt();
        int m = in.nextInt();
        arr = in.nextIntArray(n);
        //debug(Arrays.copyOf(cnt, 20));
        SegmentTree seg = new SegmentTree(n);
        
        while(m-- > 0){
            int t = in.nextInt();
            int l = in.nextInt() - 1;
            int r = in.nextInt() - 1;
            if(t == 1)
                seg.update(0, n - 1, l, r, 0, 1);
            else 
                out.println(seg.get(0, n - 1, l, r, 1));
        }
        
        out.close();
    }

    
    static class Pair implements Comparable<Pair>
    {

        int x,y;
        int i;

        Pair (int x,int y)
        {
                this.x = x;
                this.y = y;
        }

        Pair (int x,int y, int i)
        {
                this.x = x;
                this.y = y;
                this.i = i;
        }

        public int compareTo(Pair o)
        {
                return -Integer.compare(this.i, o.i);
                //return 0;
        }

        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString()
        {
            return x + " "+ y + " "+i;
        }

        /*public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }*/

    } 

    static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }

    static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }

    static long mul(long a,long b){
        long x=(a*b);
        while(x>=mod) x-=mod;
        return x;
    }

    static String rev(String s){
        StringBuilder sb=new StringBuilder(s);
        sb.reverse();
        return sb.toString();
    }

    static long gcd(long x,long y)
    {
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y)
    {
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0){
            return 1;
          }

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result >= m)
               result %= m;
            p >>=1;
            n*=n;
            if(n >= m)
                n%=m;
        }

        return result;
    }

    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

    static void debug(Object... o)
    {
            System.out.println(Arrays.deepToString(o));
    }

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
                this.stream = stream;
        }

        public int snext()
        {
                if (snumChars == -1)
                        throw new InputMismatchException();
                if (curChar >= snumChars)
                {
                        curChar = 0;
                        try
                        {
                                snumChars = stream.read(buf);
                        } catch (IOException e)
                        {
                                throw new InputMismatchException();
                        }
                        if (snumChars <= 0)
                                return -1;
                }
                return buf[curChar++];
        }

        public int nextInt()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                int res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public long nextLong()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                int sgn = 1;
                if (c == '-')
                {
                        sgn = -1;
                        c = snext();
                }
                long res = 0;
                do
                {
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
        }

        public int[] nextIntArray(int n)
        {
                int a[] = new int[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextInt();
                }
                return a;
        }

        public long[] nextLongArray(int n)
        {
                long a[] = new long[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextLong();
                }
                return a;
        }

        public String readString()
        {
                int c = snext();
                while (isSpaceChar(c))
                {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }

        public String nextLine()
        {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do
                {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
                if (filter != null)
                        return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
                return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
                public boolean isSpaceChar(int ch);
        }

    }
}