potatoes

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

char *strrev(char *str) {
    char *end = str + strlen(str) - 1;
    char *begin = str;
    while (begin < end) {
        *begin ^= *end;
        *end ^= *begin;
        *begin ^= *end;

        begin++;
        end--;
    }
    return str;
}

char *uint128tostr(__uint128_t n) {
    char *b = malloc(64 * sizeof(char));
    if (n == 0) {
        b[0] = '0';
        b[1] = 0;
        return b;
    }
    unsigned int i = 0;
    while (n) {
        b[i++] = n % 10 + '0';
        n /= 10;
    }
    b[i] = 0;
    return strrev(b);
}

__uint128_t frombase(__uint128_t num, __uint128_t radix) { /* from base 2 */
    if (radix == 2) return num;
    __uint128_t n = 1;
    __uint128_t ret = 0;
    while (num) {
        __uint128_t digit = num % 2;
        num /= 2;
        ret += digit * n;
        n *= radix;
    }
    return ret;
}

__uint128_t isprime(__uint128_t num) { /* returns 1 if prime, 0 if the number is 1, an factor otherwise */
    if (num == 1) return 0;
    if (num % 2 == 0) return 2;
    if (num % 3 == 0) return 3;
    if (num % 5 == 0) return 5;
    if (num % 7 == 0) return 7;
    if (num % 11 == 0) return 11;
    if (num < 11*11) return 1;

    __uint128_t i;
    for (i = 13; i*i <= num && i < 5000000; i += 2) { // just give up if you're trying numbers over 5000000 :P
        if (num % i == 0) return i;
    }

    return 1;
}

__uint128_t *isjamcoin(__uint128_t jamcoin) { /* returns list of divisors if is a jamcoin, NULL otherwise */
    __uint128_t *divisors = malloc(9 * sizeof(__uint128_t));

    __uint128_t i;
    for (i = 2; i <= 10; i++) {
        __uint128_t n = frombase(jamcoin, i);
        __uint128_t r = isprime(n);
        if (r > 1) {
            divisors[i-2] = r;
        } else {
            free(divisors);
            return NULL;
        }
    }

    return divisors;
}

void printjamcoins(unsigned int length, unsigned int num) {
    unsigned int count = 0;
    __uint128_t template = ((__uint128_t) 1 << (length-1)) + 1;
    __uint128_t i = 0;
    while (count < num) {
        __uint128_t jamcoin = template + ((__uint128_t) i << 1);
        __uint128_t *ret = isjamcoin(jamcoin);
        if (ret) {
            int j;
            for (j = length-1; j >= 0; j--) {
                printf("%d", (jamcoin & ((__uint128_t) 1 << j)) ? 1 : 0);
            }
            printf(" %s %s %s %s %s %s %s %s %s\n",
                    uint128tostr(ret[0]), uint128tostr(ret[1]),
                    uint128tostr(ret[2]), uint128tostr(ret[3]),
                    uint128tostr(ret[4]), uint128tostr(ret[5]),
                    uint128tostr(ret[6]), uint128tostr(ret[7]),
                    uint128tostr(ret[8]));
            /*printf(" %lu %lu %lu %lu %lu %lu %lu %lu %lu", ret[0], ret[1], ret[2], ret[3], ret[4], ret[5], ret[6], ret[7], ret[8]);*/
            count++;
        }
        i++;
    }
}

int main() {
    int _, n, j;
    scanf("%d\n%d %d", &_, &n, &j);
    printf("Case #1:\n");
    printjamcoins(n, j);
    return 0;
}