Problem:
Score : 500 points

Problem Statement

For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:

f(b,n) = n, when n < b

f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b

Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b,
and n \ {\rm mod} \ b denotes the remainder of n divided by b.

Less formally, f(b,n) is equal to the sum of the digits of n written in base b.
For example, the following hold:

f(10,\,87654)=8+7+6+5+4=30

f(100,\,87654)=8+76+54=138

You are given integers n and s.
Determine if there exists an integer b (b \geq 2) such that f(b,n)=s.
If the answer is positive, also find the smallest such b.

Constraints

1 \leq n \leq 10^{11}

1 \leq s \leq 10^{11}

n,\,s are integers.

Input

The input is given from Standard Input in the following format:

n
s

Output

If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b.
If such b does not exist, print -1 instead.

Sample Input 1

87654
30

Sample Output 1

10

Sample Input 2

87654
138

Sample Output 2

100

Sample Input 3

87654
45678

Sample Output 3

-1

Sample Input 4

31415926535
1

Sample Output 4

31415926535

Sample Input 5

1
31415926535

Sample Output 5

-1

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

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

#define BIG 2000000007

#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;

#define N_MAX 100000
#define M_MAX 200

typedef struct {
	int a;
	int b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;


typedef struct {
	ull a;
	int i;
} struct_a;

typedef struct {
	ull cost;
	int left;
	int right;
} struct_b;


const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
ull a[N_MAX];
// sll a[N_MAX];
// ull wall[N_MAX][M_MAX];
// ull b[N_MAX];
// sll b[N_MAX];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// size_t slen;
// size_t tlen;
// char s[N_MAX][M_MAX + 1];

// ull dp[N_MAX];
// sll dp[N_MAX];
// bool dp[N_MAX];
// ull dq[N_MAX];
// ull dp[N_MAX + 1][N_MAX + 1];
ull dp[N_MAX][M_MAX + 1];

// hw arr[N_MAX];
// hwll arr[N_MAX];
// hw brr[M_MAX];

// ull digitdp[102][   2][    2];
//          pos  less  carry


// struct_a arr[N_MAX * 2];
// struct_b brr[N_MAX * 2];

void swap_adj (ull *a, ull *b) {
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}

ull divide (ull a, ull b) {
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}

int digits (ull x) {
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

// int nextroute (int arr[]) {
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;

// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];

// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }

int targetdig (ull x, int index /* 1-indexed */) {
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int charcomp (const char left, const char right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int pcharcomp (const char *left, const char *right) {
	return charcomp(*left, *right);
}

int intcomp (const int left, const int right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int pintcomp (const int *left, const int *right) {
	return intcomp(*left, *right);
}

int ullcomp (const ull left, const ull right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int pullcomp (const ull *left, const ull *right) {
	return ullcomp(*left, *right);
}

int sllcomp (const sll left, const sll right) {
	if (left < right) {
		return -1;
	} else if (left > right) {
		return +1;
	} else {
		return 0;
	}
}

int psllcomp (const sll *left, const sll *right) {
	return sllcomp(*left, *right);
}

int phwAcomp (const hw *left, const hw *right) {
	return intcomp(left->a, right->a);
}

int phwBcomp (const hw *left, const hw *right) {
	return intcomp(left->b, right->b);
}

int phwABcomp (const hw *left, const hw *right) {
	int x = phwAcomp(left, right);
	if (x) return x;
	return phwBcomp(left, right);
}

int phwllAcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->a, right->a);
}

int phwllBcomp (const hwll *left, const hwll *right) {
	return sllcomp(left->b, right->b);
}

int phwllABcomp (const hwll *left, const hwll *right) {
	int x = phwllAcomp(left, right);
	if (x) return x;
	return phwllBcomp(left, right);
}

int bitlet (char c) {
	return (1 << (c - 'a'));
}

ull ullabs (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sllabs (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll nibutanlobo (bool (*func)(sll arg), sll ok, sll ng) {
	while (sllabs(ok, ng) > 1) {
		sll med = (ok + ng) / 2;
		if (func(med)) {
			ok = med;
		} else {
			ng = med;
		}

		// printf("debug: [%lld %lld)\n", ok, ng);
	}

	if (!func(ok)) return ok * 2 - ng;
	return ok;
}


bool isbeaten (sll x) {
	int i;
	ull required = 0;
	for (i = 0; i < n; i++) {
		sll remainhp = a[i] - vub * x;
		if (remainhp > 0) {
			required += (remainhp - 1) / (vua - vub) + 1;
		}
	}
	return (required <= x);
}

ull solve () {
	sll i, j, ki;
	ull result = 0;
	// sll result = 0;
	ull sum = 0;
	// qsortの際には"p"ullcompを使う

	if (m == 1) {
		result = n;
		goto success;
	}

	if (n == m) {
		result = n + 1;
		goto success;
	} else if (n < m) {
		goto fail;
	} else {
		ull radix, dig1;
		for (i = 1; i * (i + 1) <= n && i < m; i++) {
			dig1 = m - i;
			if ((n - dig1) % i) continue;
			radix = (n - dig1) / i;
			if (i >= radix || dig1 >= radix) continue;

			result = radix;
		}
	}

	for (i = 2; i * i <= n; i++) {
		ull num = n;
		sum = 0;
		while (num) {
			sum += (num % i);
			num /= i;
		}

		if (sum == m) {
			result = i;
			goto success;
		}
	}

	if (result) goto success;
	goto fail;

	printf("%lld\n", result);
	// puts(s);

	return 0;

	success:
	// puts("First");
	printf("%llu\n", result);
	return 0;

	fail:
	puts("-1");
	return 1;
}

int main (void) {
	int i, j;
	int x, y;

	// scanf("%llu%llu", &h, &w);
	scanf("%llu%llu", &n, &m);
	// scanf("%llu%llu", &vua, &vub);
	// scanf("%s", s);
	// slen = strlen(s);
	// scanf("%s", t);
	// tlen = strlen(t);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &a[i]);
	// }
	// for (i = 0; i < m; i++) {
	// 	scanf("%lld", &b[i]);
	// }

	solve();

	// for (i = 0; i < n; i++) {
	// 	// scanf("%llu%llu", &vua, &vub);
	// 	scanf("%s", s);
	// 	solve();
	// }

	return 0;
}