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

public class Main {

    void solve() throws IOException {
        simple_ints = new ArrayList<>();
        int size = 1000001;
        r = new boolean[size];
        for (int i = 2; i < size; i++) if (!r[i]) for (int j = 2; j * i < size; j++) r[i * j] = true;
        for (int i = 2; i < size; i++) if (!r[i]) simple_ints.add(i);
        d = new int[size];
        for (int i = 2; i < size; i++) d[i] = getD(0, i);
        d[1] = 1;
        int n = readInt();
        int m = readInt();
        int[] a = readIntArray(n);
        TreeSet<Integer> st = new TreeSet<>();
        for (int i = -1; i < n; i++) st.add(i);
        for (int i = 0; i < n; i++) if (a[i] <= 2) st.remove(i);
        int lo, hi, pref;
        Fenwik fen = new Fenwik(a);
        while (m-- > 0) {
            int type = readInt();
            lo = readInt() - 1;
            hi = readInt() - 1;
            if (type == 1) {
                int h = st.floor(hi);
                while (h >= lo) {
                    pref = a[h];
                    a[h] = d[a[h]];
                    fen.inc(h, a[h] - pref);
                    if (a[h] < 3) st.remove(h);
                    h = st.floor(h - 1);
                }
            } else out.println(fen.getSum(hi) - (lo > 0 ? fen.getSum(lo - 1) : 0));
        }
    }

    int[] d;
    ArrayList<Integer> simple_ints;
    boolean[] r;

    int getD(int index, int value) {
        if (d[value] != 0) return d[value];
        int k = 1;
        while (value % simple_ints.get(index) == 0) {
            k++;
            value /= simple_ints.get(index);
        }
        if (value == 1) return k;
        if (!r[value]) return (k << 1);
        d[value] = getD(index + 1, value);;
        k *= d[value];
        return k;
    }


    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;

    Main() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
        tok = new StringTokenizer("");
    }

    void run() throws IOException {
        solve();
        out.close();
    }


    class Fenwik {
        private long[] t;
        private int length;

        Fenwik(int[] a) {
            this.length = a.length + 100;
            this.t = new long[length];
            for (int i = 0; i < a.length; ++i) this.inc(i, a[i]);
        }

        void inc(int i, int delta) {
            for (; i < this.length; i = i | (i + 1)) t[i] += delta;
        }

        long getSum(int r) {
            long sum = 0;
            for (; r >= 0; r = (r & (r + 1)) - 1) sum += this.t[r];
            return sum;
        }
    }

    String delimiter = " ";

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;
            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readIntArray(int b) {
        int a[] = new int[b];
        for (int i = 0; i < b; i++)
            try {
                a[i] = readInt();
            } catch (IOException e) {
                e.printStackTrace();
            }
        return a;
    }

    int[] readSortedIntArray(int size) throws IOException {
        Integer[] array = new Integer[size];
        for (int index = 0; index < size; ++index) array[index] = readInt();
        Arrays.sort(array);
        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) sortedArray[index] = array[index];
        return sortedArray;
    }

    int[] sortedIntArray(int size, int[] array) throws IOException {
        for (int index = 0; index < size; ++index) array[index] = readInt();
        Arrays.sort(array);
        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) sortedArray[index] = array[index];
        return sortedArray;
    }

    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) min = Math.min(min, value);
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) max = Math.max(max, value);
        return max;
    }

    long minLong(long... values) {
        long min = Long.MAX_VALUE;
        for (long value : values) min = Math.min(min, value);
        return min;
    }

    long maxLong(long... values) {
        long max = Long.MIN_VALUE;
        for (long value : values) max = Math.max(max, value);
        return max;
    }

    boolean checkIndex(int index, int size) {
        return (0 <= index && index < size);
    }

    int abs(int a) {
        if (a < 0) return -a;
        return a;
    }
}