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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <fstream>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <stack>
#include <queue>
#include <complex>
#include <set>
#include <list>
#include <iomanip>
#include <map>
#include <memory.h>



using namespace std;
static const double EPS = 1e-9;
typedef long long ll;
typedef unsigned long long ull;
#define FOR(i,n) for(int i=0;i<(int)n;++i)
#define FORNUM(p, x) for (int num = p; num < (int)(x); ++num)
#define FORI(p, x) for (int i = p; i < (int)(x); ++i)
#define FORJ(p, x) for (int j = p; j < (int)(x); ++j)
#define FORK(p, x) for (int k = p; k < (int)(x); ++k)
#define FORL(p, x) for (int l = p; l < (int)(x); ++l)

typedef pair<int,int>P;
#define INF 1000000000
 
struct edge { 
	int from, to; 
	edge (int from, int to){
		this->from=from; this->to=to;
	}
};
 
int V,E;
typedef vector<edge> edges;
vector<edges> G;

ll n, s;

ll f(ll b, ll n) {
	ll ret;
	if (n < b)
		return n;
	ret = f(b, n / b) + n % b;
	return ret;
}

ll solve() {
	ll ans;
	if (n == s)
		return n + 1;
	if (s > n)
		return -1;
	for (int b = 2; b*b <= n; b++) {
		if (s == f(b, n)) {
			return b;
		}
	}
	for (int p = 1; p*p <= (n - s); p++) {
		ll b = 1 + (n - s) / p;
		if (s == f(b, n)) {
			ans = min(b, ans);
				

		}
	}
	return ans;
}

int main(){
	cin >> n >> s;
	
	cout << solve() << endl;
	return 0;
}