Problem:
Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

/*
......................................................................................................................................
.....................................  ________ ____ __________________________________________ .....................................
..................................... /  _____/|    |   \      \__    ___/\_   _____/\______   \.....................................
...................................../   \  ___|    |   /   |   \|    |    |    __)_  |       _/.....................................
.....................................\    \_\  \    |  /    |    \    |    |        \ |    |   \.....................................
..................................... \______  /______/\____|__  /____|   /_______  / |____|_  /.....................................
.....................................        \/                \/                 \/         \/ .....................................
......................................................................................................................................
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....................................................................................:.................................................
......................................................................................................................................
......................................................................................................................................
 */
import java.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.pow;

import static java.lang.String.format;


public class Main {
    final static long MOD=1000_000_000L+7;
    public static void main(String[] args) {
        Scanner scanner=new Scanner();
        final int n=scanner.nextInt();
        final int m=scanner.nextInt();
        int mm=m;
        int[] x=new int[100000];
        for(int i=2;i<x.length||mm>1;i++){
            while(mm%i==0){
                x[i]++;
                mm/=i;
            }
        }
        if(mm==m){
            put(n);
            return;
        }
        long ans=1;
        for(int i=2;i<x.length;i++){
            if(x[i]==0)continue;
            ans*=CalcComb.calcComb(n-1+x[i],n-1);
            ans%=MOD;
        }
        if(mm>1){
            ans*=n;
            ans%=MOD;
        }
        put(ans);
    }
    public static class CalcComb{
        private final static long MOD=1000_000_000+7;
        public static long calcComb(int a,int b){
            if(b>a-b)return calcComb(a,a-b);
            long ansMul=1;
            long ansDiv=1;
            //p:素数
            //a^(p-1)%p=1
            //a^(p-2)%p=1/a
            //(ansMul/ansDiv)%MOD==(ansMul*ansDiv^(p-2))%MOD
            for(int i=0;i<b;i++){
                ansMul*=a-i;
                ansDiv*=i+1;
                ansMul%=MOD;
                ansDiv%=MOD;
            }
            return ansMul*ModPow.modPow(ansDiv,MOD-2)%MOD;
        }
    }

    public static class ModPow{
        private final static long MOD=1000_000_000+7;
        //(x^y)%MOD
        public static long modPow(long x,long y){
            if(y==0)return 1;
            if(y%2==0){
                long halfY=y/2;
                long halfModPow = modPow(x,halfY)%MOD;
                return halfModPow*halfModPow%MOD;
            }else{
                return x*modPow(x,y-1)%MOD;
            }
        }

    }

    public static int upper_bound(long[] a,long val){
        return upper_bound(a,0,a.length,val);
    }
    public static int upper_bound(long[] a,int l,int r,long val){
        if(r-l==1){
            if(a[l]>val) return l;
            return r;
        }
        int mid=(l+r)/2;
        if(a[mid]>val){
            return upper_bound(a,l,mid,val);
        }else{
            return upper_bound(a,mid,r,val);
        }
    }
    public static <T> int upper_bound(T[] a,int l,int r,T val,Comparator<T> comparator){
        if(r-l==1){
            if(comparator.compare(a[l],val)>0) return l;
            return r;
        }
        int mid=(l+r)/2;
        if(comparator.compare(a[mid],val)>0){
            return upper_bound(a,l,mid,val,comparator);
        }else{
            return upper_bound(a,mid,r,val,comparator);
        }
    }
    public static int lower_bound(long[] a,long val){
        return lower_bound(a,0,a.length,val);
    }
    public static int lower_bound(long[] a,int l,int r,long val){
        if(r-l==1){
            if(a[l]<val) return r;
            return l;
        }
        int mid=(l+r)/2;
        if(a[mid]<val){
            return lower_bound(a,mid,r,val);
        }else{
            return lower_bound(a,l,mid,val);
        }

    }

    public static <T> int lower_bound(T[] a,int l,int r,T val,Comparator<T> comparator){
        if(r-l==1){
            if(comparator.compare(a[l],val)<0) return r;
            return l;
        }
        int mid=(l+r)/2;
        if(comparator.compare(a[mid],val)<0){
            return lower_bound(a,mid,r,val,comparator);
        }else{
            return lower_bound(a,l,mid,val,comparator);
        }
    }


    public static void print(Object object){
        System.out.print(object);
    }
    public static void put(Object object) {
        System.out.println(object);
    }
    public static void put(){
        System.out.println();
    }

    final static private class Scanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    final static private class FixedLongPair {
        final private long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        public long getX() {
            return x;
        }

        public long getY() {
            return y;
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            boolean result=super.equals(obj);
            if(obj.getClass()!=this.getClass()){
                return false;
            }
            FixedLongPair pair=(FixedLongPair)obj;
            if(this.x==pair.x&&this.y==pair.y) return true;
            return false;
        }

        @Override
        public String toString() {
            return String.format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedIntPair {
        final private int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int getX() {
            return x;
        }

        public int getY() {
            return y;
        }

        @Override
        public int hashCode() {
            return x+y;
        }

        @Override
        public boolean equals(Object obj) {
            boolean result=super.equals(obj);
            if(obj.getClass()!=this.getClass()){
                return false;
            }
            FixedIntPair pair=(FixedIntPair) obj;
            if(this.x==pair.x&&this.y==pair.y) return true;
            return false;
        }

        @Override
        public String toString() {
            return String.format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Tuple<T,V>{
        //immutabl1でないことに注意(T,Vがmutableの場合変更可能)
        final private T t;
        final private V v;
        Tuple(T t,V v){
            this.t=t;
            this.v=v;
        }

        public T getT() {
            return t;
        }

        public V getV() {
            return v;
        }

        @Override
        public int hashCode() {
            return (t.hashCode()+v.hashCode());
        }

        @Override
        @SuppressWarnings("unchecked")
        public boolean equals(Object obj) {
            if(obj.getClass()!=this.getClass()){
                return false;
            }
            Tuple<T,V> tuple=(Tuple<T, V>) obj;
            return tuple.t.equals(this.t)&&tuple.v.equals(this.v);
        }

        @Override
        public String toString() {
            return String.format("<Tuple>=<%s,%s>",t,v);
        }
    }
    final static private class Util {
        static long gcd(long a,long b){
            //最大公約数　
            if(a%b==0)return b;
            return gcd(b,a%b);
        }
        static long lcm(long a,long b){
            //最小公倍数
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static long kaijoMod(int n,int mod){
            if(n<1) return -1;
            long result=1;
            for(int i=n;i>1;i--){
                result*=i;
                result%=mod;
            }
            return result;
        }
        static <T extends Comparable<T>> Map<T,Integer> count(List<T> list){
            //副作用
            Collections.sort(list);
            Map<T,Integer> result=new HashMap<>();
            int l=0,r=0;
            while(l<list.size()){
                while(r<list.size()-1&&list.get(r).equals(r+1)){
                    r++;
                }
                result.put(list.get(r),r-l+1);
                r++;
                l=r;
            }
            return result;

        }
        static Map<Integer,Integer> count(int[] array){
            //副作用
            Arrays.sort(array);
            Map<Integer,Integer> result=new HashMap<>();
            int l=0,r=0;
            while(l<array.length){
                while(r<array.length-1&&array[r]==array[r+1]){
                    r++;
                }
                result.put(array[l],r-l+1);
                r++;
                l=r;
            }
            return result;
        }
        static <T> String toStringBWS(Iterable<T> iterable){
            Iterator<T> ite=iterable.iterator();
            return toStringBWS(ite);
        }
        static <T> String toStringBWS(Iterator<T> ite){
            StringBuilder sb=new StringBuilder();
            sb.append(ite.next());
            while(ite.hasNext()){
                sb.append(" ");
                sb.append(ite.next());
            }
            return sb.toString();
        }
        static int[] factoringInPrimeNumbers(long n,int size){
            //素因数分解
            //sizeがnに比べて小さい場合完全に素因数分解出来ていない可能性がある
            int[] result=new int[size];
            for(int i=2;n>1&&i< result.length;i++){
                while(n%i==0){
                    result[i]++;
                    n/=i;
                }
            }
            return result;

        }
        public static long min(long... longs){
            if(longs.length==0)throw new IllegalArgumentException("Argument.length==0");
            long min=Long.MAX_VALUE;
            for(int i=0;i<longs.length;i++){
                min=Math.min(min,longs[i]);
            }
            return min;
        }
        public static long max(long... longs){
            if(longs.length==0)throw new IllegalArgumentException("Argument.length==0");
            long max=Long.MIN_VALUE;
            for(int i=0;i<longs.length;i++){
                max=Math.max(max,longs[i]);
            }
            return max;
        }
    }
}