//Problem F - Bet or Not (dynamic programming)

#include <iostream.h>
#include <stdlib.h>

void ComputeChances(int,int,int*, double[41][53]);

void main()
{
	int n,i,j;
	double P;
	char S[5];
	int Board[53], t, m;
	double Chances[41][53];

	cin>>n;
	for(j=0;j<n;j++)
	{
	  cin>>m>>t;
	  
	  Board[0]=Board[m]=Board[m+1]=0;
	  for(i=1;i<=m;i++)
	  {
		cin>>S;
		if(S[0]=='L')
			Board[i]=100;
		else
			Board[i]=atoi(S);
	  }

	  ComputeChances(t,m,Board,Chances);

	  P= Chances[t][0];
	  
      cout.setf(ios::fixed,ios::floatfield);
      cout.precision(4);
	  if(P>0.5)
		  cout<<"Bet for. "<< P << endl;
	  else if(P<0.5)
		  cout<<"Bet against. "<< P << endl;
	  else //P=0.5
		  cout<<"Push. "<< P << endl;
	}
}

void ComputeChances(int t, int m, int * Board, double Chances[41][53])
{
	int i, p, p1,p2,move;         // Board[0]=start, Board[m+1]=end
	double leftchance, rightchance;

	//do 0 moves
	for(i=0;i<=m;i++)
		Chances[0][i]=0;
	Chances[0][m+1]= Chances[0][m+2]=1;
	//do 1 moves
	for(i=0;i<=m-1;i++)
	{
		p1=i+1; p2=i+2;
		if(p1>m) leftchance=1;
			else if(Board[p1]==100)   //lose a turn
				leftchance=0;
			else {
				p1=p1+Board[p1];
				leftchance=Chances[0][p1];
			}
		if(p2>m) rightchance=1;
			else if(Board[p2]==100)   //lose a turn
				rightchance=0;
			else {
				p2=p2+Board[p2];
				rightchance=Chances[0][p2];
			}
		Chances[1][i]=leftchance/2+rightchance/2;
	}
	if(m>2)
	{
		if(Board[m]>0 && Board[m]!=100)
			Chances[1][m-1]=1;
		else
			Chances[1][m-1]=0.5;
	}
	//do the m-1 and m columns
	for(i=1;i<=t;i++)
		Chances[i][m+1]=Chances[i][m]=Chances[i][m+2]=1;

	//now fill in the rest of the table
	for(move=2;move<=t;move++)
		for(p=0;p<m;p++)
		{
			p1=p+1;
			p2=p+2;

			if(p1>m) leftchance=1;
			else if(Board[p1]==100)   //lose a turn
				leftchance=Chances[move-2][p1];
			else {
				p1=p1+Board[p1];
				leftchance=Chances[move-1][p1];
			}
			if(p2>m) rightchance=1;
			else if(Board[p2]==100)   //lose a turn
				rightchance=Chances[move-2][p2];
			else {
				p2=p2+Board[p2];
				rightchance=Chances[move-1][p2];
			}

			Chances[move][p]=leftchance/2+rightchance/2;
		}


}