#!/bin/sh
# n 種のガチャポンなり食玩なりを
# m 回でコンプリートする確率
# http://aquarius10.cse.kyutech.ac.jp/~otabe/shokugan/
awk '
function combination(n, r,   i, x, y) {
	x = y = 1;
	for (i = 0; i < r; i++) {
		x *= n--;
		y *= (i + 1);
	}
	return x / y;
}

function ipow(x, n,   i, y) {
	y = 1;
	for (i = 0; i < n; i++) {
		y *= x;
	}
	return y;
}

function nn_p(ntypes, times,   i, sign, sigma) {
	sign = (ntypes % 2 == 0) ? -1 : 1;
	sigma = 0;
	for (i = 0; i < ntypes; i++) {
		sigma += sign * combination(ntypes - 1, i) * ipow((i + 1) / ntypes, times - 1);
		sign = sign < 0 ? 1 : -1;
	}
	return sigma;
}

BEGIN {
	myname = ENVIRON["_"];
	if (ARGC != 3) {
		printf("usage: %s n m\nCalculate probability of complete n types by m times.\n", myname) > "/dev/stderr";
	}
	else {
		ntypes = ARGV[1];
		times = ARGV[2];
		printf("%d %d = %.13g\n", ntypes, times, nn_p(ntypes, times));
	}
}' "$@"