Asymmetric random walk problem

Asymmetric random walk problem:

P(X_i = 1) = p, and
P(X_i = -1) = 1-p for all i>0.

let S_n = sum_{i=0}^n X_i, S_0=0, and
S_* = max{S_0, S_1, ..., S_n} where 1<=k<=n.

let n, m, b are even positive integers
such that b<=m, m<=n, and 2m-b<=n,

then
P(S_*>=m, S_n=b) = ?

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