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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        int[] getDivisorsCount(int n) { // divisors for all number up to n inclusive
            int[] divisors = new int[n + 1];
            for (int i = 1; i * i < divisors.length; i++) {
                for (int j = i * i; j < divisors.length; j += i) {
                    divisors[j]++; // adds 1 as divisor currently
                    if (j / i != i) divisors[j]++;
                }
            }
            return divisors;
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int m = in.readInt();
            int[] a = IOUtils.readIntArray(in, n);
            int[] divisors = getDivisorsCount(ArrayUtils.maxElement(a));
            TreeSet<Integer> canChange = new TreeSet<>();
            for (int i = 0; i < a.length; i++) {
                if (a[i] != divisors[a[i]]) {
                    canChange.add(i);
                }
            }
            FenwickTree ft = new FenwickTree(a.length);
            for (int i = 0; i < a.length; i++) {
                ft.add(i, a[i]);
            }
            for (int query = 0; query < m; query++) {
                int type = in.readInt();
                int l = in.readInt() - 1;
                int r = in.readInt() - 1;
                if (type == 1) {
                    while (true) {
                        Integer closest = canChange.ceiling(l);
                        if (closest != null && closest <= r) {
                            ft.add(closest, -a[closest]);
                            a[closest] = divisors[a[closest]];
                            ft.add(closest, a[closest]);
                            if (a[closest] == divisors[a[closest]]) {
                                canChange.remove(closest);
                            }
                        } else break;
                        l = closest + 1;
                    }
                } else if (type == 2) {
                    out.printLine(ft.get(l, r));
                } else throw new RuntimeException();
            }
        }
    }
    static class IOUtils {
        public static int[] readIntArray(InputReader in, int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = in.readInt();
            }
            return array;
        }
    }
    static abstract class IntAbstractStream implements IntStream {
        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }

        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }

        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }
    }
    static interface IntCollection extends IntStream {
        public int size();
    }
    static interface IntReversableCollection extends IntCollection {
    }
    static class ArrayUtils {
        public static int maxElement(int[] array) {
            return new IntArray(array).max();
        }
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

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

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

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

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        public IntIterator intIterator();
        default public Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }
        default public int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }
        default public int max() {
            int result = Integer.MIN_VALUE;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                int current = it.value();
                if (current > result) {
                    result = current;
                }
            }
            return result;
        }
    }
    static class FenwickTree {
        private final long[] value;

        public FenwickTree(int size) {
            value = new long[size];
        }

        public long get(int from, int to) {
            return get(to) - get(from - 1);
        }

        private long get(int to) {
            to = Math.min(to, value.length - 1);
            long result = 0;
            while (to >= 0) {
                result += value[to];
                to = (to & (to + 1)) - 1;
            }
            return result;
        }

        public void add(int at, long value) {
            while (at < this.value.length) {
                this.value[at] += value;
                at = at | (at + 1);
            }
        }
    }
    static class IntArray extends IntAbstractStream implements IntList {
        private int[] data;

        public IntArray(int[] arr) {
            data = arr;
        }

        public int size() {
            return data.length;
        }

        public int get(int at) {
            return data[at];
        }

        public void removeAt(int index) {
            throw new UnsupportedOperationException();
        }
    }
    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);
        public abstract void removeAt(int index);
        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && at < size();
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }
    }
    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }
    }
    static interface IntIterator {
        public int value() throws NoSuchElementException;
        public boolean advance();
        public boolean isValid();
    }
}