For nonnegative integers s and r, let C(s,r) = s!/[r!(s − r)!] if r ≤ s, and C(s,r) = 0 if r > s. For positive integers m and n, let g(m,n) = Σ(p=0 to m+n) f(m,n,p)/C(n+p,p), where for any nonnegative integer p, f(m,n,p) = Σ(i=0 to p) C(m,i)C(n+i,p)C(p+n,p−i). Then which of the following statements is/are TRUE?