def solve(N, P, C): mod = 10 ** 9 + 7 ps = [2-2, 3-2, 5-2, 7-2, 11-2, 13-2] cs = [4-4, 6-4, 8-4, 9-4, 10-4, 12-4] distp = get_dist(ps, P) distc = get_dist(cs, C) dist = merge_dists(distp, distc) dist = [0] * (2 * P + 4 * C - 1) + dist + [0] mat = get_mat(dist) matN = matrix_pow(mat, N - 1, mod) return finalize(matN, dist, mod) def get_dist(qs, Q): ''' qs を合計Q個使った和が、何通りの作り方があるかを返す。 dp[i][n][s]: qs[:i] までを合計n個使って合計sとなる組み合わせの数 qs[i] = qi とすると dp[i + 1][0][0] = 1 dp[i + 1][0][s] = 0, s > 0 dp[i + 1][1][s] = 1 if s == qi else dp[i][1][s] dp[i + 1][n][s] = dp[i][n][s] + dp[i + 1][n - 1][s - qi] [i] を落とすと、 dp[n][s] += dp[n-1][s-n] で更新する。 ''' len_dp = qs[-1] * Q + 1 dp = [[0] * len_dp for n in range(Q + 1)] dp[0][0] = 1 for q in qs: for n in range(1, Q + 1): current_dp = dp[n] prev_dp = dp[n - 1] for s in range(q, q * n + 1): current_dp[s] += prev_dp[s - q] return dp[Q] def merge_dists(distp, distc): mod = 10 ** 9 + 7 len_p = len(distp) len_c = len(distc) dist = [0] * (len_p + len_c - 1) for i, pi in enumerate(distp): for ij, cj in enumerate(distc, i): dist[ij] += pi * cj dist[ij] %= mod return dist def get_mat(dist): n = len(dist) mat = [dist[:]] for i in range(n - 1): row = [0] * n row[i] = 1 mat.append(row) return mat def mult(mat1, mat2, mod): nrow = len(mat1) ncol = len(mat2[0]) mat = [[0] * ncol for r in range(nrow)] for c in range(ncol): col2 = [row[c] for row in mat2] for r, row1 in enumerate(mat1): mat[r][c] = sum(a * b for a, b in zip(row1, col2)) % mod return mat def get_identity_matrix(n): matI = [[0] * n for i in range(n)] for i in range(n): matI[i][i] = 1 return matI def matrix_pow(mat, p, mod): n = len(mat) matR = get_identity_matrix(n) while p: if p & 1: matR = mult(mat, matR, mod) mat = mult(mat, mat, mod) p >>= 1 return matR def finalize(mat, dist, mod): n = len(dist) vec = [[0] for i in range(n)] vec[0][0] = 1 vec_n = mult(mat, vec, mod) result = 0 for i, v_row in enumerate(vec_n): result += sum(dist[i:]) * v_row[0] result %= mod return result def print_mat(mat): for row in mat: print(row) if __name__ == '__main__': N, P, C = map(int, input().split()) print(solve(N, P, C))