Let $S={X1,X2,X3…...Xk}$ where $0<=Xi<=1$ for $1<=i<=k$ and $\sum_{i=1}^{k}X_i = 1$.

Also $0<=P(x)<=1$ for all $x\in S$. Given that $\sum_{i=1}^{k}P(X_i) = 1$.

Let us say T =Max $(1/{(\sum_{i=1}^{k}(X_i)^2 )} )$

Also, $F(x) = \sum_{i=1}^{k}P(X_i) log(1/P(X _i))$ (log with base 2).

Given that $Max(F(x)) = 13$.

Find $(T!)$mod $1000000007$