import numpy as np from numpy.fft import fft, ifft def trans(f, size, shift): mask = (1 << shift) - 1 ff = np.zeros(size, dtype=np.complex128) ff[:len(f)] = ((f & mask) + (f >> shift) * 1j) / 2.0 ff = fft(ff) ffrc = np.concatenate((ff[0:1], ff[-1:0:-1])).conj() return ff, ffrc def itrans(f, s, mod, shift): a = ifft(f[0])[:s] lo = a.real.round().astype(np.int64) mid = a.imag.round().astype(np.int64) hi = ifft(f[1]).real.round().astype(np.int64)[:s] ret = (lo + ((mid % mod) << shift) + ((hi % mod) << (2 * shift))) % mod return ret def fmul(r1, i1, r2, i2): return (r1 * (r2 + i2) + i1 * r2, -i1 * i2) def poly_mul_mod(f, g, mod, shift=15): s = len(f) + len(g) - 1 size = 1 << ((2 * s - 1).bit_length() - 1) ff, ffrc = trans(f, size, shift) fg, fgrc = trans(g, size, shift) ffr, ffi = ff + ffrc, ff - ffrc fgr, fgi = fg + fgrc, fg - fgrc return itrans(fmul(ffr, ffi, fgr, fgi), s, mod, shift) def iterate(n, f, g, mod, shift=15): sf, sg = len(f), len(g) size = 1 << ((2 * (2 * sg - 1) - 1).bit_length() - 1) sh = size // 2 ff, ffrc = trans(f, size, shift) fg, fgrc = trans(g, size, shift) fmg = np.concatenate((fg[sh:], fg[:sh])) fmgrc = np.concatenate((fgrc[sh:], fgrc[:sh])) ffr, ffi = ff + ffrc, ff - ffrc fgr, fgi = fg + fgrc, fg - fgrc fmgr, fmgi = fmg + fmgrc, fmg - fmgrc lo, hi = fmul(ffr, ffi, fmgr, fmgi) if not n & 1: lo, hi = (lo[:sh] + lo[sh:]) * 0.5, (hi[:sh] + hi[sh:]) * 0.5 else: a = np.arange(sh) * (2 * np.pi / size) vs = (np.cos(a) + 1j * np.sin(a)) * 0.5 lo, hi = (lo[:sh] - lo[sh:]) * vs, (hi[:sh] - hi[sh:]) * vs numer = itrans((lo, hi), (sg + sf - (n & 1)) // 2, mod, shift) denom = itrans(fmul(fgr[:sh], fgi[:sh], fgr[sh:], fgi[sh:]), sg, mod, shift) return numer, denom def nth(n, numer, denom, mod): while n > 0: numer, denom = iterate(n, numer, denom, mod) n >>= 1 return numer[0] def solve(): import sys Ps = np.array([2, 3, 5, 7, 11, 13], dtype=np.int) Cs = np.array([4, 6, 8, 9, 10, 12], dtype=np.int) mod = 10 ** 9 + 7 def gene(ds, T): dp = np.zeros((T + 1, ds[-1] * T + 1), dtype=np.int) dp[0, 0] = 1 o = ds[0] for di in range(6): d = ds[di] for t in range(T): dp[t+1, d+o*t:d*(t+1)+1] = \ (dp[t+1, d+o*t:d*(t+1)+1] + dp[t, o*t:d*t+1]) % mod return dp[T, :] for line in sys.stdin: N, P, C = map(int, line.split()) denom = poly_mul_mod(gene(Ps, P), gene(Cs, C), mod) denom = (mod - denom) % mod denom[0] = 1 numer = np.cumsum(denom, dtype=np.int64) % mod print(nth(N + len(denom) - 1, numer, denom, mod)) solve()