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.math.BigInteger;
import java.util.*;
public class l {
    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMMMM      MMMMMM      OOO      OOO        SSSS   SSS     EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEE           MMMM MMM  MMM MMMM    OOO          OOO    SSSS       SSS   EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM  MMMMMM  MMMM   OOO            OOO   SSSS             EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM  OOO              OOO   SSSSSSS         EEEEE          /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO      SSSSSS       EEEEEEEEEEE    /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO         SSSSSSS   EEEEEEEEEEE    /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM   OOO            OOO              SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM    OOO          OOO     SSS       SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM      OOO      OOO        SSS    SSSS    EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int q = sc.nextInt();
        int[] in = new int[n + 1];
        TreeSet<Integer> ts = new TreeSet<>();
        FenwickTree fn = new FenwickTree(n);
        int max=2;
        for(int i = 1; i <= n; i++) {
            in[i] = sc.nextInt();
            fn.point_update(i,in[i]);
            if (in[i]>2)ts.add(i);
            max=Math.max(max,in[i]);
        }
//        for (int i =2;i<=10;i++){
//            System.out.print(fun[i]+" ");
//        }
//        System.out.println();
        sieve(max);
        ArrayList<Integer>removed= new ArrayList<>();
        while (q-->0){
            if (sc.nextInt()==2){
                int l = sc.nextInt();
                int r= sc.nextInt();
                pw.println(fn.rsq(l,r));
            }
            else {
                int l = sc.nextInt();
                int r = sc.nextInt();
                for (int id:ts.subSet(l,r+1)){
                    fn.point_update(id,fun[in[id]]-in[id]);
                    in[id]=fun[in[id]];
                    if (in[id]<=2)removed.add(id);
                }
                if (removed.size()>0){
                    for(int ll:removed){
                        ts.remove(ll);
                    }
                    removed.clear();
                }
            }
        }
        pw.flush();
    }
    static class FenwickTree {
        int n;
        long[] ft;
 
        FenwickTree(int size) {
            n = size;
            ft = new long[n + 1];
        }
 
        long rsq(int b) //O(log n)
        {
            long sum = 0;
            while (b > 0) {
                sum += ft[b];
                b -= b & -b;
            }        //min?
            return sum;
        }
 
        long rsq(int a, int b) {
            return rsq(b) - rsq(a - 1);
        }
 
        void point_update(int k, int val)    //O(log n), update = increment
        {
            while (k <= n) {
                ft[k] += val;
                k += k & -k;
            }        //min?
        }
    }
    static int[]isComposite,fun;
    static void sieve(int N){
        isComposite= new int[N+1];
        fun= new int[N+1];
        isComposite[0]=isComposite[1]=1;
        Arrays.fill(fun,1);
        for (int i =2;i<=N;i++)
            if (isComposite[i]==0){
            fun[i]=2;
            for (int j =i+i;j<=N;j+=i){
                isComposite[j]=1;
                int x =j;
                int e=1;
                while (x%i==0){
                    x/=i;
                    e++;
                }
                fun[j]*=e;
            }
            }
    }
 
    static long gcd(long a, long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
 
    static int inver(long x, int mod) {
        int a = (int) x;
        int e = (mod - 2);
        int res = 1;
        while (e > 0) {
            if ((e & 1) == 1) {
                //System.out.println(res*a);
                res = (int) ((1l * res * a) % mod);
            }
            a = (int) ((1l * a * a) % mod);
            e >>= 1;
        }
        //out.println(res+" "+x);
        return res % mod;
    }
 
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
 
        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }
 
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
 
        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
 
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
 
        public String nextLine() throws IOException {
            return br.readLine();
        }
 
        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }
 
        public boolean ready() throws IOException {
            return br.ready();
        }
    }
 
 
}