prison

There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....

Do the following N times:

* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.



Find the number that was originally assigned to the prisoner released in the Nth operation.

Constraints

* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.



Input Format

Input is given from standard input in the following format.


N k


Output Format

Print the answer in one line.

Sample Input 1


4 2


Sample Output 1


7


Sample Input 2


13


Sample Output 2


0


Sample Input 3


100000 100000


Sample Output 3


99999






Example

Input

4 2


Output

7
//#define __USE_MINGW_ANSI_STDIO 0
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VL;
typedef vector<VL> VVL;
typedef pair<int, int> PII;

#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
#define MP make_pair
#define PB push_back
#define MOD 1000000007
#define INF (1LL<<30)
#define LLINF (1LL<<60)
#define PI 3.14159265359
#define EPS 1e-12
//#define int ll

signed main(void)
{
	int n, k;
	cin >> n >> k;
	
	ll low = 0, high = 1e18;
	while(high-low>1) {
		ll mid = (high+low)/2, tmp = mid;
		//cout << high << " " << mid << " " << low << endl;
		bool flag = false;
		REP(i, n-1) {
			tmp -= (tmp-1)/k+1;
			if(tmp <= 0) flag = true;
		}
		if(flag) low = mid;
		else high = mid;
	}
	cout << low << endl;

	return 0;
}