The number "zero" is called "love" (or "l'oeuf" to be precise, literally means "egg" in French), for example when denoting the zero score in a game of tennis. 

Aki is fond of numbers, especially those with trailing zeros. For example, the number 9200 has two trailing zeros. Aki thinks the more trailing zero digits a number has, the prettier it is.

However, Aki believes, that the number of trailing zeros of a number is not static, but depends on the base (radix) it is represented in. Thus, he considers a few scenarios with some numbers and bases. And now, since the numbers he used become quite bizarre, he asks you to help him to calculate the beauty of these numbers.

Given two integers n and b (in decimal notation), your task is to calculate the number of trailing zero digits in the b-ary (in the base/radix of b) representation of n ! ([factorial](https://en.wikipedia.org/wiki/Factorial) of n). 

Input

The only line of the input contains two integers n and b (1 ≤ n ≤ 10^{18}, 2 ≤ b ≤ 10^{12}).

Output

Print an only integer — the number of trailing zero digits in the b-ary representation of n!

Examples

Input

6 9


Output

1


Input

38 11


Output

3


Input

5 2


Output

3


Input

5 10


Output

1

Note

In the first example, 6!_{(10)} = 720_{(10)} = 880_{(9)}.

In the third and fourth example, 5!_{(10)} = 120_{(10)} = 1111000_{(2)}.

The representation of the number x in the b-ary base is d_1, d_2, …, d_k if x = d_1 b^{k - 1} + d_2 b^{k - 2} + … + d_k b^0, where d_i are integers and 0 ≤ d_i ≤ b - 1. For example, the number 720 from the first example is represented as 880_{(9)} since 720 = 8 ⋅ 9^2 + 8 ⋅ 9 + 0 ⋅ 1.

You can read more about bases [here](https://en.wikipedia.org/wiki/Radix).

import java.io.*;
import java.math.BigInteger;
import java.util.*;


public class Main {
    private static Scanner sc;
    private static Printer pr;
    private static long aLong=(long)(Math.pow(10,9)+7);
    private static void solve() throws IOException {
        long N = sc.nextLong();
        long B = sc.nextLong();
        long ans = N;
        for (long j = 2; j * j <= B; j++) {
            if (B % j == 0) {
                long count = 0;
                while (B % j == 0) {
                    count++;
                    B /= j;
                }
                long c = 0;
                long k = N;
                while (k / j > 0) {
                    c += k / j;
                    k /= j;
                }
                ans = Math.min(ans, c / count);
            }
        }
        if (B > 1) {
            long j = B;
            if (B % j == 0) {
                long p = 0;
                while (B % j == 0) {
                    p++;
                    B /= j;
                }
                long c = 0;
                long k = N;
                while (k / j > 0) {
                    c += k / j;
                    k /= j;
                }
                ans = Math.min(ans, c / p);
            }
        }
        pr.println(ans);
    }
    public static long []primeFactor(int n){
        long []prime=new long[n+1];
        prime[1]=1;
        for (int i=2;i<=n;i++)
            prime[i]=((i&1)==0)?2:i;
        for (int i=3;i*i<=n;i++){
            if (prime[i]==i){
                for (int j=i*i;j<=n;j+=i){
                    if (prime[j]==j)
                        prime[j]=i;
                }
            }
        }
        return prime;
    }
    public static StringBuilder binaryradix(long number){
        StringBuilder builder=new StringBuilder();
        long remainder;
        while (number!=0) {
            remainder = number % 2;
            number >>= 1;
            builder.append(remainder);
        }
        builder.reverse();
        return builder;
    }
    public static int binarySearch(long[] a, int index,long target) {
            int l = index;
            int h = a.length - 1;
            while (l<=h) {
                int med = l + (h-l)/2;
                if(a[med] - target <= target) {
                    l = med + 1;
                }
                else h = med  - 1;
            }
            return h;
    }
    public static int val(char c){
        return c-'0';
    }
    public static long gcd(long a,long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
        private static class Pair implements Comparable<Pair> {
            long x;
            long y;

            Pair() {
                this.x = 0;
                this.y = 0;
            }

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

            @Override
            public boolean equals(Object obj) {
                if (this == obj) {
                    return true;
                }
                if (obj == null) return false;
                Pair other = (Pair) obj;
                if (this.x == other.x && this.y == other.y) {
                    return true;
                }
                return false;
            }

            @Override
            public int compareTo(Pair other) {
                if (this.x != other.x) return Long.compare(this.x, other.x);
                return Long.compare(this.y*other.x, this.x*other.y);
            }
    }

    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pr = new Printer(System.out);
        solve();

        pr.close();
       // sc.close();
    }
    private static class Scanner {
        BufferedReader br;

        Scanner (InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        private boolean isPrintable(int ch) {
            return ch >= '!' && ch <= '~';
        }

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

        private int nextPrintable() {
            try {
                int ch;
                while (!isPrintable(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }

                return ch;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        String next() {
            try {
                int ch = nextPrintable();
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (isPrintable(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        int nextInt() {
            try {
                // parseInt from Integer.parseInt()
                boolean negative = false;
                int res = 0;
                int limit = -Integer.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Integer.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                int multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        long nextLong() {
            try {
                // parseLong from Long.parseLong()
                boolean negative = false;
                long res = 0;
                long limit = -Long.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Long.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                long multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        float nextFloat() {
            return Float.parseFloat(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            try {
                int ch;
                while (isCRLF(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (!isCRLF(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
//				throw new NoSuchElementException();
            }
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class List {
        String Word;
        int length;

        List(String Word, int length) {
            this.Word = Word;
            this.length = length;
        }
    }
    private static class Printer extends PrintWriter {
        Printer(PrintStream out) {
            super(out);
        }
    }
}