Problem: Aoki is in search of Takahashi, who is missing in a one-dimentional world. Initially, the coordinate of Aoki is 0, and the coordinate of Takahashi is known to be x, but his coordinate afterwards cannot be known to Aoki.

Time is divided into turns. In each turn, Aoki and Takahashi take the following actions simultaneously:

* Let the current coordinate of Aoki be a, then Aoki moves to a coordinate he selects from a-1, a and a+1.

* Let the current coordinate of Takahashi be b, then Takahashi moves to the coordinate b-1 with probability of p percent, and moves to the coordinate b+1 with probability of 100-p percent.




When the coordinates of Aoki and Takahashi coincide, Aoki can find Takahashi. When they pass by each other, Aoki cannot find Takahashi.

Aoki wants to minimize the expected number of turns taken until he finds Takahashi. Find the minimum possible expected number of turns.

Constraints

* 1 ≦ x ≦ 1,000,000,000
* 1 ≦ p ≦ 100
* x and p are integers.

Input

The input is given from Standard Input in the following format:


x
p


Output

Print the minimum possible expected number of turns. The output is considered correct if the absolute or relative error is at most 10^{-6}.

Examples

Input

3
100


Output

2.0000000


Input

6
40


Output

7.5000000


Input

101
80


Output

63.7500000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>                        
#define pb push_back                            
#define mp make_pair                            
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)((x).size())
#define jonathan ios_base::sync_with_stdio(0)
#define livingston cin.tie(0)
using namespace std;                            
                                                
void yes() {cout << "Yes" << endl;}                                               
void no() {cout << "No" << endl;}                                                        
                                                
int dx[] = {1, 0, -1, 0, -1, -1, 1, 1};         
int dy[] = {0, 1, 0, -1, -1, 1, -1, 1}; 

const int INF = 1e9 + 9;
const long long LINF = 1e18 + 8;
const double EPS = 1e-9;
const long long MOD = 1e9 + 7; //998244353
const double PI = acos(-1);

void solve() {
    long long x, p; cin >> x >> p;
    cout << fixed << setprecision(6) << (double)((x + 1) / 2 * 100.0 / p) << endl;
} 

int main() {
    jonathan; 
    livingston;
    solve();
    return 0;
}