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 JAVA):

Solution:
import java.io.IOException; 
import java.io.InputStream; 
import java.io.PrintWriter; 
import java.util.*; 
 

class Main{ 

	static void solve(){
		int x = ni();
		double p = ni()/100.0;
		double ans = 0;
		if(x%2==0)ans=(double)x/(2*p);
		else{
			ans=1;
			ans += (x-1)/2;
			ans += ((1-p)*((double)x+1))/(p*2);
		}
		out.println(ans);
 
	} 
 
 
 
 
	 public static void main(String[] args){ 
		 solve(); 
		 out.flush(); 
	 } 
	 private static InputStream in = System.in; 
	 private static PrintWriter out = new PrintWriter(System.out); 
 
	 static boolean inrange(int y, int x, int h, int w){ 
		 return y>=0 && y<h && x>=0 && x<w; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static<T extends Comparable> int lower_bound(List<T> list, T key){ 
		 int lower=-1;int upper=list.size(); 
		 while(upper - lower>1){ 
		 int center =(upper+lower)/2; 
		 if(list.get(center).compareTo(key)>=0)upper=center; 
		 else lower=center; 
		 } 
		 return upper; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static <T extends Comparable> int upper_bound(List<T> list, T key){ 
		 int lower=-1;int upper=list.size(); 
		 while(upper-lower >1){ 
		 int center=(upper+lower)/2; 
		 if(list.get(center).compareTo(key)>0)upper=center; 
		 else lower=center; 
		 } 
		 return upper; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static <T extends Comparable> boolean next_permutation(List<T> list){ 
		 int lastIndex = list.size()-2; 
		 while(lastIndex>=0 && list.get(lastIndex).compareTo(list.get(lastIndex+1))>=0)--lastIndex; 
		 if(lastIndex<0)return false; 
		 int swapIndex = list.size()-1; 
		 while(list.get(lastIndex).compareTo(list.get(swapIndex))>=0)swapIndex--; 
		 T tmp = list.get(lastIndex); 
		 list.set(lastIndex++, list.get(swapIndex)); 
		 list.set(swapIndex, tmp); 
		 swapIndex = list.size()-1; 
		 while(lastIndex<swapIndex){ 
		 tmp = list.get(lastIndex); 
		 list.set(lastIndex, list.get(swapIndex)); 
		 list.set(swapIndex, tmp); 
		 ++lastIndex;--swapIndex; 
		 } 
		 return true; 
	 } 
	 private static final byte[] buffer = new byte[1<<15]; 
	 private static int ptr = 0; 
	 private static int buflen = 0; 
	 private static boolean hasNextByte(){ 
		 if(ptr<buflen)return true; 
		 ptr = 0; 
		 try{ 
			 buflen = in.read(buffer); 
		 } catch (IOException e){ 
			 e.printStackTrace(); 
		 } 
		 return buflen>0; 
	 } 
	 private static int readByte(){ if(hasNextByte()) return buffer[ptr++]; else return -1;} 
	 private static boolean isSpaceChar(int c){ return !(33<=c && c<=126);} 
	 private static int skip(){int res; while((res=readByte())!=-1 && isSpaceChar(res)); return res;} 
 
	 private static double nd(){ return Double.parseDouble(ns()); } 
	 private static char nc(){ return (char)skip(); } 
	 private static String ns(){ 
		 StringBuilder sb = new StringBuilder(); 
		 for(int b=skip();!isSpaceChar(b);b=readByte())sb.append((char)b); 
		 return sb.toString(); 
	 } 
	 private static int[] nia(int n){ 
		 int[] res = new int[n]; 
		 for(int i=0;i<n;++i)res[i]=ni(); 
		 return res; 
	 } 
	 private static long[] nla(int n){ 
		 long[] res = new long[n]; 
		 for(int i=0;i<n;++i)res[i]=nl(); 
		 return res; 
	 } 
	 private static int ni(){ 
		 int res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	 } 
	 private static long nl(){ 
		 long res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	} 
}