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)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
//#pragma comment(linker, "/STACK:1024000000,1024000000")

using namespace std;

#define ll long long
#define SZ(x) ((int)(x).size()) 
#define ALL(v) (v).begin(), (v).end()
#define foreach(i, v) for (__typeof((v).begin()) i = (v).begin(); i != (v).end(); ++ i)
#define reveach(i, v) for (__typeof((v).rbegin()) i = (v).rbegin(); i != (v).rend(); ++ i) 
#define REP(i,a,n) for ( int i=a; i<int(n); i++ )
#define FOR(i,a,n) for ( int i=n-1; i>= int(a);i-- )
#define lson rt<<1, L, m
#define rson rt<<1|1, m, R
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define mp(x, y) make_pair(x, y)
#define pb(x) push_back(x)
#define fi first
#define se second
#define CLR(a, b) memset(a, b, sizeof(a))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)

ll n, s;

bool ok(ll b){
    if(b < 2) return false;
    ll x = n;
    ll sum = 0;
    while(x){
        sum += x % b;
        x /= b;
    }
    return sum == s;
}
int main(){
#ifdef ac
	freopen("in.txt","r",stdin);
#endif
	//freopen("out.txt","w",stdout);
    scanf("%lld%lld", &n, &s);
    ll sn = sqrt(n);
    REP(i, 2, sn + 1){
        if(ok(i)){
            printf("%d\n", i);
            return 0;
        }
    }
    FOR(q, 1, sn){
        if((n - s + q) % q == 0){
            if(ok((n - s + q) / q)){
                printf("%lld\n", (n - s) / q + 1);
                return 0;
            }
        }
    }
    puts("-1");
    return 0;
}