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: Accepted)

/* template.cpp [[[ */
#include <bits/stdc++.h>
using namespace std;
#define get_macro(a, b, c, d, name, ...) name
#define rep(...) get_macro(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(...) get_macro(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define rep1(n) rep2(i_, n)
#define rep2(i, n) rep3(i, 0, n)
#define rep3(i, a, b) rep4(i, a, b, 1)
#define rep4(i, a, b, s) for (ll i = (a); i < (ll)(b); i += (ll)s)
#define rrep1(n) rrep2(i_, n)
#define rrep2(i, n) rrep3(i, 0, n)
#define rrep3(i, a, b) rrep4(i, a, b, 1)
#define rrep4(i, a, b, s) for (ll i = (ll)(b) - 1; i >= (ll)(a); i -= (ll)s)
#define each(x, c) for (auto &&x : c)
#define fs first
#define sc second
#define all(c) begin(c), end(c)
using ui = unsigned;
using ll = long long;
using ul = unsigned long long;
using ld = long double;
const int inf = 1e9 + 10;
const ll inf_ll = 1e18 + 10;
const ll mod = 1e9 + 7;
const ll mod9 = 1e9 + 9;
const int dx[]{-1, 0, 1, 0, -1, 1, 1, -1};
const int dy[]{0, -1, 0, 1, -1, -1, 1, 1};
template<class T, class U> void chmin(T &x, const U &y){ x = min<T>(x, y); }
template<class T, class U> void chmax(T &x, const U &y){ x = max<T>(x, y); }
struct prepare_ { prepare_(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(12); } } prepare__;
/* ]]] */

int main(){
  ll n, s;
  cin >> n >> s;
  if (n == s) cout << n + 1 << endl, exit(0);
  ll res = inf_ll;
  rep(i, 2, n){
    if (i * i > n) break;
    ll x = n, t = 0;
    while (x) t += x % i, x /= i;
    if (s == t) chmin(res, i);
  }
  rep(i, 1, n){
    if (i * i >= n) break;
    if ((n - (s - i)) % i) continue;
    ll b = (n - (s - i)) / i;
    if (s - i >= b) continue;
    if (i * b + s - i != n) continue;
    if (s - i < 0) continue;
    chmin(res, b);
  }
  cout << (res == inf_ll ? -1 : res) << endl;
}