#include<iostream>using namespace std;long long a[51][51]; //表示概率的分子 long long b[51][51]; //表示概率的分母 //将(i,j) 处的概率的1/2传递到(i+1,t) void transmit(int i, int j, int t){long long temp = b[i][j]<<1;if(a[i+1][t]){if(b[i+1][t] != temp){if(b[i+1][t] < temp){ while(b[i+1][t] < temp) { a[i+1][t] <<= 1; b[i+1][t] <<= 1; } a[i+1][t] += a[i][j];}else{long long temp_a = a[i][j];while(temp < b[i+1][j]){temp <<= 1;temp_a <<= 1;}a[i+1][t] += temp_a;}}else{a[i+1][t] += a[i][j];}}else{a[i+1][t]=a[i][j];b[i+1][t]=temp;}}long long gcd(long long a, long long b){long long temp;while(b != 0){temp = a;a = b;b = temp % b;}return a;}int main(){int n,m;char ch;//输入数据 cin>>n>>m;//计算概率a[0][0]=1;b[0][0]=1;for(int i=0; i<n; i++) for(int j=0; j<=i; j++) {cin>>ch;if(!a[i][j]) continue;if(ch=='*') // 钉子在{//更新a[i+1][j] b[i+1][j] transmit(i, j, j);//更新a[i+1][j+1] b[i+1][j+1]transmit(i, j, j+1);}else //钉子不在 {a[i+2][j+1]=a[i][j];b[i+2][j+1]=b[i][j];} } long long temp_a = a[n][m]; long long temp_b = b[n][m]; if(!temp_a) cout<<"0/1"<<endl; else { long g = gcd(temp_a, temp_b); while(g != 1) {temp_a /= g;temp_b /= g;g = gcd(temp_a, temp_b); } cout<<temp_a<<"/"<<temp_b<<endl; } return 0;}
