import java.util.Arrays; import java.util.Random; class FactorL { static long[][] factorX(long n, int[] primes) { long[][] ret = new long[20][2]; int rp = 0; for(int p : primes){ if((long)p * p > n)break; int i; for(i = 0;n % p == 0;n /= p, i++); if(i > 0){ ret[rp][0] = p; ret[rp][1] = i; rp++; } } if(n == 1)return Arrays.copyOf(ret, rp); // P^2 long sq = (long)Math.sqrt(n); for(long u = Math.max(2, sq-2);u <= sq+2;u++){ if(u*u == n){ ret[rp][0] = u; ret[rp][1] = 2; rp++; return Arrays.copyOf(ret, rp); } } // Prime if(doMirrorRabin(n)){ ret[rp][0] = n; ret[rp][1] = 1; rp++; return Arrays.copyOf(ret, rp); } // P*Q long f = rho(n); if(f == -1)throw new ArithmeticException(); if(f > n/f)f = n/f; ret[rp][0] = f; ret[rp][1] = 1; rp++; ret[rp][0] = n/f; ret[rp][1] = 1; rp++; return Arrays.copyOf(ret, rp); } public static long mul(long a, long b, long mod) { a %= mod; long ret = 0; int x = 63-Long.numberOfLeadingZeros(b); for(;x >= 0;x--){ ret += ret; if(ret >= mod)ret -= mod; if(b<<~x<0){ ret += a; if(ret >= mod)ret -= mod; } } return ret; } public static boolean doMirrorRabin(long n) { // int[] P = {2, 7, 61}; // n<4759123141 int[] P = {2,3,5,7,11,13,17,19,23}; // n=long int s = Long.numberOfTrailingZeros(n-1); long d = n-1>>s; outer: for(int a : P){ if(a >= n)continue; long mul = a; long ad = 1; for(long e = d;e > 0;e>>>=1){ if((e&1)==1)ad = mul(ad, mul, n); mul = mul(mul, mul, n); } if(ad == 1)continue; for(int r = 0;r < s;r++){ if(ad == n-1)continue outer; ad = mul(ad, ad, n); } return false; } return true; } static long rho(long n) { Random gen = new Random(); for(int u = 0;u < 100;u++){ long ran = (gen.nextLong()&Long.MAX_VALUE) % n; long x = 2, y = 2, d = 1; while(d == 1){ x = (mul(x, x, n)+ran)%n; y = (mul(y, y, n)+ran)%n; y = (mul(y, y, n)+ran)%n; d = gcd(Math.abs(x-y), n); } if(d < n)return d; } return -1; } public static long gcd(long a, long b) { while (b > 0){ long c = a; a = b; b = c % b; } return a; } public static int[] sieveEratosthenes(int n) { if(n <= 32){ int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 }; for(int i = 0;i < primes.length;i++){ if(n < primes[i]){ return Arrays.copyOf(primes, i); } } return primes; } int u = n + 32; double lu = Math.log(u); int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)]; ret[0] = 2; int pos = 1; int[] isp = new int[(n + 1) / 32 / 2 + 1]; int sup = (n + 1) / 32 / 2 + 1; int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 }; for(int tp : tprimes){ ret[pos++] = tp; int[] ptn = new int[tp]; for(int i = (tp - 3) / 2;i < tp << 5;i += tp) ptn[i >> 5] |= 1 << (i & 31); for(int i = 0;i < tp;i++){ for(int j = i;j < sup;j += tp) isp[j] |= ptn[i]; } } // 3,5,7 // 2x+3=n int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 }; int h = n / 2; for(int i = 0;i < sup;i++){ for(int j = ~isp[i];j != 0;j &= j - 1){ int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27]; int p = 2 * pp + 3; if(p > n) break; ret[pos++] = p; for(int q = pp;q <= h;q += p) isp[q >> 5] |= 1 << (q & 31); } } return Arrays.copyOf(ret, pos); } } public class Main { //v = 1.2024234005160768 //e = 65657059 static int[] primes = FactorL.sieveEratosthenes(2000000); static double EPS = 0.000000000000001; private static void solve() { long n = nl(); long m = nl(); long d = div(n, m); double f = factor(n); String ret = calc(f, m, d); System.out.println(ret); } private static double factor(double n) { double ret = Math.log(Math.PI * 2 / (n + 1)) /2 + Math.log((n + 1) / Math.E) * (n + 1); return ret / Math.log(10); } private static String calc(double logFactorN, long m, long d) { double ret = logFactorN; long e1 = (long)(ret + EPS); ret -= e1; double div = d * Math.log10(m); long e2 = (long)(div + EPS); div -= e2; e1 -= e2; ret -= div; double v = Math.pow(10, ret); while (v < 1) { e1 --; v *= 10; } return String.format("%.4fe%d\n", v, e1); } private static long div(long n, long m) { long[][] f = FactorL.factorX(m, primes); long[] count = new long[f.length]; for (int i = 0; i < f.length; i ++) { long x = n; while (x > 0) { count[i] += x / f[i][0]; x /= f[i][0]; } } long min = Long.MAX_VALUE; for (int i = 0; i < f.length; i ++) { min = Math.min(count[i] / f[i][1], min); } return min; } public static void main(String[] args) { new Thread(null, new Runnable() { @Override public void run() { long start = System.currentTimeMillis(); String debug = args.length > 0 ? args[0] : null; if (debug != null) { try { is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug)); } catch (Exception e) { throw new RuntimeException(e); } } reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768); solve(); out.flush(); tr((System.currentTimeMillis() - start) + "ms"); } }, "", 64000000).start(); } private static java.io.InputStream is = System.in; private static java.io.PrintWriter out = new java.io.PrintWriter(System.out); private static java.util.StringTokenizer tokenizer = null; private static java.io.BufferedReader reader; public static String next() { while (tokenizer == null || !tokenizer.hasMoreTokens()) { try { tokenizer = new java.util.StringTokenizer(reader.readLine()); } catch (Exception e) { throw new RuntimeException(e); } } return tokenizer.nextToken(); } private static double nd() { return Double.parseDouble(next()); } private static long nl() { return Long.parseLong(next()); } private static int[] na(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) a[i] = ni(); return a; } private static char[] ns() { return next().toCharArray(); } private static long[] nal(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++) a[i] = nl(); return a; } private static int[][] ntable(int n, int m) { int[][] table = new int[n][m]; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { table[i][j] = ni(); } } return table; } private static int[][] nlist(int n, int m) { int[][] table = new int[m][n]; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { table[j][i] = ni(); } } return table; } private static int ni() { return Integer.parseInt(next()); } private static void tr(Object... o) { if (is != System.in) System.out.println(java.util.Arrays.deepToString(o)); } }