Graded Betti numbers of powers of path ideals of paths

Let I_n,m = (x_1⋯ x_m,x_2 ⋯ x_m+1,…,x_n+1x_n+2⋯ x_n+m) be the m-path ideal of a path of length n + m-1 over a polynomial ring S = k[x_1,…,x_n+m]. We compute all the graded Betti numbers of all powers of I_n,m.