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.util.*;
import java.io.*;
import java.lang.*;
public  class c2 
{

	
	public static long mod = (int)Math.pow(10, 9) + 7;
    
	
    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        // Code starts..

       
        long n = in.nextLong();
        long b = in.nextLong();
        ArrayList<Long> list = new ArrayList<>();
        
        long ans=Long.MAX_VALUE;
        for(long i=2;i*i<=b;i++){
            int cnt=0;
            while(b%i==0){
                cnt++;
                b/=i;
            }
            if(cnt>0)
                ans=Math.min(fun(n,i)/cnt,ans);
            
        }
        if(b!=1){
            ans=Math.min(fun(n,b),ans);
        }
       
    
        
        pw.println(ans);
        
        
        
        
        
		
		
		
        pw.flush();
        pw.close();
    }
    


     public static long fun(long n,long x)
     {
		    long ans=0;
		    while(n>0){
		        n/=x;
		        ans+=n;
		    }
		    return ans;
		}
    
    
    public static long pow(long x, long n, long M) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }
    
    
    
   
    

    public static long getFloor(long[] a, long x)
	{
		int left = 0, right = a.length - 1;

		long floor = -1;
		long fi = -1;
		while (left <= right)
		{
			int mid = (left + right) / 2;

			if (a[mid] - x == 0) {
				return mid;
			}

			else if (x - a[mid] < 0) {
				right = mid - 1;
			}
			else {
				floor = a[mid];
				fi = mid;
				left = mid + 1;
			}
		}

		return fi;
	}
    
    
    
    public static void factSieve(int[] fact, long n)
    {

        for (int i = 2; i <= n; i += 2)
            fact[i] = 2;

        for (int i = 3; i <= n; i += 2) {
            if (fact[i] == 0) {
                fact[i] = i;

                for (int j = i; (long) j * i <= n; j++) {
                    fact[(int) ((long) i * j)] = i;
                }
            }
        }

        /*
         * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
         * 
         * }
         */
    }

    
    public static int gcd(int p2, int p22)
    {
        if (p2 == 0)
            return (int) p22;
        return gcd(p22 % p2, p2);
    }

    public static void nextGreater(long[] a, int[] ans)
    {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] < a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] >= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static void nextGreaterRev(long[] a, int[] ans)
    {

        int n = a.length;
        int[] pans = new int[n];
        Arrays.fill(pans, -1);
        long[] arev = new long[n];
        for (int i = 0; i < n; i++)
            arev[i] = a[n - 1 - i];

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < n; i++) 
        {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (arev[s] < arev[i]) {
                    pans[s] = n - i - 1;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (arev[s] >= arev[i])
                    stk.push(s);
            }

            stk.push(i);

        }

        // for(int i=0; i<n; i++)
        // System.out.print(pans[i]+" ");

        for (int i = 0; i < n; i++)
            ans[i] = pans[n - i - 1];

        return;

    }

    public static void nextSmaller(long[] a, int[] ans)
    {

        Stack<Integer> stk = new Stack<>();
        stk.push(0);

        for (int i = 1; i < a.length; i++) {

            if (!stk.isEmpty()) {
                int s = stk.pop();
                while (a[s] > a[i]) {
                    ans[s] = i;
                    if (!stk.isEmpty())
                        s = stk.pop();
                    else
                        break;
                }
                if (a[s] <= a[i])
                    stk.push(s);
            }

            stk.push(i);

        }
        return;

    }

    public static long lcm(int[] numbers) 
    {
        long lcm = 1;
        int divisor = 2;
        while (true) {
            int cnt = 0;
            boolean divisible = false;
            for (int i = 0; i < numbers.length; i++) {
                if (numbers[i] == 0) {
                    return 0;
                } else if (numbers[i] < 0) {
                    numbers[i] = numbers[i] * (-1);
                }
                if (numbers[i] == 1) {
                    cnt++;
                }
                if (numbers[i] % divisor == 0) {
                    divisible = true;
                    numbers[i] = numbers[i] / divisor;
                }
            }
            if (divisible) {
                lcm = lcm * divisor;
            } else {
                divisor++;
            }
            if (cnt == numbers.length) {
                return lcm;
            }
        }
    }

    public static long fact(long n)
    {

        long factorial = 1;
        for (int i = 1; i <= n; i++) {
            factorial *= i;
        }
        return factorial;
    }


    public static long choose(long total, long choose)
    {
        if (total < choose)
            return 0;
        if (choose == 0 || choose == total)
            return 1;
        return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
    }

    public static int[] suffle(int[] a, Random gen)
    {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }

    public static int[] sufflesort(int[] a) 
    {
        int n = a.length;
        Random gen = new Random();
        for (int i = 0; i < n; i++) {
            int ind = gen.nextInt(n - i) + i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
        return a;
    }
    
    
    
    
    public static int floorSearch(int arr[], int low, int high, int x) 
    {
        if (low > high)
            return -1;

        if (x > arr[high])
            return high;
        int mid = (low + high) / 2;

        if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
            return mid - 1;

        if (x < arr[mid])
            return floorSearch(arr, low, mid - 1, x);

        return floorSearch(arr, mid + 1, high, x);
    }

    public static void swap(int a, int b) {
        int temp = a;
        a = b;
        b = temp;
    }

    public static ArrayList<Integer> primeFactorization(int n)
    {
        ArrayList<Integer> a = new ArrayList<Integer>();
        for (int i = 2; i * i <= n; i++) {
            while (n % i == 0) {
                a.add(i);
                n /= i;
            }
        }
        if (n != 1)
            a.add(n);
        return a;
    }
    
    
    

    public static void sieve(boolean[] isPrime, int n) 
    {
        for (int i = 1; i < n; i++)
            isPrime[i] = true;

        isPrime[0] = false;
        isPrime[1] = false;

        for (int i = 2; i * i < n; i++) {
            if (isPrime[i] == true) {
                for (int j = (2 * i); j < n; j += i)
                    isPrime[j] = false;
            }
        }
    }

   /* public static int lowerbound(long[] a, long c2) 
    {
        int i = Collections.binarySearch(a, c2);
        if (i < 0)
            i = -(i + 2);
        return i;

    }*/
    
/*    public static int lowerboundArray(long[] a, long c2) 
    {
        int i = Arrays.flo(a, c2);
        
        
        if (i < 0)
            i = -(i + 2);
        return i;

    }*/

    public static int uperbound(ArrayList<Integer> list, int c2) 
    {
        int i = Collections.binarySearch(list, c2);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    public static int uperboundArray(long[] a, long l)
    {
        int i = Arrays.binarySearch(a, l);
        if (i < 0)
            i = -(i + 1);
        return i;

    }

    
    public static int GCD(int a, int b)
    {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static long GCD(long a, long b) 
    {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }

    public static int d1;
    public static int p1;
    public static int q1;
    
    public static void extendedEuclid(int A, int B)
    {
        if (B == 0) {
            d1 = A;
            p1 = 1;
            q1 = 0;
        } else {
            extendedEuclid(B, A % B);
            int temp = p1;
            p1 = q1;
            q1 = temp - (A / B) * q1;
        }
    }

    public static long LCM(long a, long b) {
        return (a * b) / GCD(a, b);
    }

    public static int LCM(int a, int b) {
        return (a * b) / GCD(a, b);
    }

    public static int binaryExponentiation(int x, int n) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = x * x;
            n = n / 2;
        }
        return result;
    }

    public static int[] countDer(int n) {
        int der[] = new int[n + 1];

        der[0] = 1;
        der[1] = 0;
        der[2] = 1;

        for (int i = 3; i <= n; ++i)
            der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

        // Return result for n
        return der;
    }

    static long binomialCoeff(int n, int k) {
        long C[][] = new long[n + 1][k + 1];
        int i, j;

        // Calculate value of Binomial Coefficient in bottom up manner
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= Math.min(i, k); j++) {
                // Base Cases
                if (j == 0 || j == i)
                    C[i][j] = 1;

                // Calculate value using previosly stored values
                else
                    C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }

        return C[n][k];
    }

    public static long binaryExponentiation(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = result * x;
            x = (x % mod * x % mod) % mod;
            n = n / 2;
        }
        return result;
    }

    public static int modularExponentiation(int x, int n, int M) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static long modularExponentiation(long x, long n, long M) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1)
                result = (result * x) % M;
            x = (x * x) % M;
            n = n / 2;
        }
        return result;
    }

    public static long modInverse(long q, long M) {
        return modularExponentiation(q, M - 2, M);
    }

    public static long sie(long A, long M) {
        return modularExponentiation(A, M - 2, M);
    }

    public static boolean isPrime(int n) {

        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }

        return true;
    }

    static class pair implements Comparable<pair>

    {
        Long x, y;

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

        public int compareTo(pair o) {
        	int result = -y.compareTo(o.y);
            if (result == 0)
            	result = x.compareTo(o.x);

            return result;
        }

        public String toString() {
            return x + " " + y;
        }

        public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair) o;
                return p.x == x && p.y == y;
            }
            return false;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }

    }

    static class triplet implements Comparable<triplet> {
        Long x, y, z;

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

        public int compareTo(triplet o) {
            int result = x.compareTo(o.x);
            if (result == 0)
                result = y.compareTo(o.y);
            if (result == 0)
                result = z.compareTo(o.z);

            return result;
        }

        public boolean equlas(Object o) {
            if (o instanceof triplet) {
                triplet p = (triplet) o;
                return x == p.x && y == p.y && z == p.z;
            }
            return false;
        }

        public String toString() {
            return x + " " + y + " " + z;
        }

        public int hashCode() {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
        }
    }

    
    
    
    
    
    /*
     * static class node implements Comparable<node>
     * 
     * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
     * 
     * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
     * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
     * result; }
     * 
     * @Override public int compareTo(node o) { // TODO Auto-generated method stub
     * return 0; } }
     */



    static class InputReader 
	{
		 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) 
		{
			this.stream = stream;
		}
 
		public int snext() 
		{
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) 
			{
				curChar = 0;
				try 
				{
					snumChars = stream.read(buf);
				} 
				catch (IOException e) 
				{
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt() 
	    {
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			int sgn = 1;
			if (c == '-')
		    {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong()
	    {
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) 
		{
			int a[] = new int[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextInt();
			}
			return a;
		}
 
		public String readString()
	    {
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public String nextLine() 
		{
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) 
		{
			return c == '\n' || c == '\r' || c == -1;
		}
 
		public interface SpaceCharFilter
	    {
			public boolean isSpaceChar(int ch);
		}
	}
	
	



}