/*
 * 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
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>

static int verbose;
static int *mark;
static long long ok;
static long long total;

static void
oain(int lv, int v[], int ntypes, int times)
{
	if (lv == 0) {
		int i, j;
		int sum = 0;
		for (i = 0; i < ntypes; i++)
			mark[i] = 0;
		for (j = 0; j < times; j++)
			mark[v[j]] = 1;
		for (i = 0; i < ntypes; i++)
			sum += mark[i];
		if (sum == ntypes) {
			ok++;
			if (verbose) {
				for (i = 0; i < times; i++) {
					printf("%d", v[i]);
				}
				printf("\n");
			}
		}
		total++;
		return;
	}
	else {
		int i;
		for (i = 0; i < ntypes; i++) {
			v[times - lv] = i;
			oain(lv - 1, v, ntypes, times);
		}
	}
}/* oain */

static int
nain(int ntypes, int times)
{
	int err = -1;
	int *v = malloc(sizeof(*v) * times);
	int vbyte = (sizeof(*v) * times);
	mark = malloc(sizeof(*mark) * ntypes);
	if (v != NULL && mark != NULL) {
		memset(v, '\0', vbyte);
		oain(times, v, ntypes, times);
		printf("%lld/%lld=%.16g\n", ok, total, (double)ok / total);
		err = 0;
	}
	else {
		perror("malloc");
	}
	return err;
} 


int
main(int argc, char *argv[])
{
	int ex = 1, ch, show_usage = 0;
	while ((ch = getopt(argc, argv, "vV")) != EOF) {
		switch (ch) {
		default:
		case 'V':
			show_usage++;
			break;
		case 'v':
			verbose++;
			break;
		}/* switch */
	}/* while */
	if (argc - optind != 2 || show_usage) {
		fprintf(stderr, "usage: %s [-v] n m\nCalculate probability of complete n types by m times.\n", argv[0]);
	}
	else {
		int ntype = strtol(argv[optind], NULL, 0);
		int times = strtol(argv[optind + 1], NULL, 0);
		ex = nain(ntype, times) < 0;
	}
	return ex;
}/* main */