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: Runtime Error)

#include<iostream>
#include<cstdio>
#include<vector>
#include<string>
#include<cstring>
#include<functional>
#include<stack>
#include<queue>
#include <iomanip>
#include<map>
#include<limits>
#include<cmath>
#include<algorithm>
#include<bitset>
#include<utility>
#include<complex>
#include<cstdlib>
#include<set>
#include<cctype>

#define DBG cerr << '!' << endl;
#define REP(i,n) for(ll (i) = (0);(i) < (n);++i)
#define rep(i,s,g) for(ll (i) = (s);(i) < (g);++i)
#define rrep(i,s,g) for(ll (i) = (s);i >= (g);--(i))
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define SHOW1d(v,n) {for(int W = 0;W < (n);W++)cerr << v[W] << ' ';cerr << endl << endl;}
#define SHOW2d(v,i,j) {for(int aaa = 0;aaa < i;aaa++){for(int bbb = 0;bbb < j;bbb++)cerr << v[aaa][bbb] << ' ';cerr << endl;}cerr << endl;}
#define ALL(v) v.begin(),v.end()
#define Decimal fixed<<setprecision(10)

using namespace std;

typedef long long ll;
typedef vector<int> iv;
typedef vector<iv> iiv;
typedef vector<string> sv;

ll func(ll b,ll n)
{
	if(n == 0)return 0;
	return func(b,n/b) + (n % b);
}

int main()
{
	ll n,s;cin >> n >> s;
	
	if(s == n)
	{
		cout << n+1 << endl;
		return 0;
	}
	
	for(ll i = 2;i*i <= n;i++)
	{
		if(func(i,n) == s)
		{
			cout << i << endl;
			return 0;
		}
	}
	ll ans = 100000000000000LL;
	for(ll i = 1;i*i <= n;i++)
	{
		if((n-s)%i==0 && (n-s)/i!=0)
		{
			ll tmp = (n-s)/i + 1;
			if(func(tmp,n) == s)ans = min(ans,tmp);
		}
	}
	
	if(ans == 100000000000000LL)
	{
		cout << -1 << endl;
		return 0;
	}
	else
	{
		cout << ans << endl;
		return 0;
	}
	
	return 0;
}