class BinomialCoefficient: def __init__(self, m): self.MOD = m self.factorization = self._factorize(m) self.facs = [] self.invs = [] self.coeffs = [] self.pows = [] for p, pe in self.factorization: fac = [1]*pe for i in range(1, pe): fac[i] = fac[i-1]*(i if i % p else 1) % pe inv = [1]*pe inv[-1] = fac[-1] for i in range(1, pe)[::-1]: inv[i-1] = inv[i]*(i if i % p else 1) % pe self.facs.append(fac) self.invs.append(inv) # coeffs c = self._modinv(m // pe, pe) self.coeffs.append(m//pe*c % m) # pows powp = [1] while powp[-1]*p != pe: powp.append(powp[-1]*p) self.pows.append(powp) def __call__(self, n, k): if k < 0 or k > n: return 0 if k == 0 or k == n: return 1 % self.MOD res = 0 for i, (p, pe) in enumerate(self.factorization): res += self._choose_pe(n, k, p, pe, self.facs[i], self.invs[i], self.pows[i]) * self.coeffs[i] res %= self.MOD return res def _E(self, n, k, r, p): res = 0 while n: n //= p k //= p r //= p res += n - k - r return res def _choose_pe(self, n, k, p, pe, fac, inv, powp): r = n-k e0 = self._E(n, k, r, p) if e0 >= len(powp): return 0 res = powp[e0] if (p != 2 or pe == 4) and self._E(n//(pe//p), k//(pe//p), r//(pe//p), p) % 2: res = pe-res while n: res = res * fac[n % pe] % pe * inv[k % pe] % pe * inv[r % pe] % pe n //= p k //= p r //= p return res def _factorize(self, N): factorization = [] for i in range(2, N+1): if i*i > N: break if N % i: continue c = 0 while N % i == 0: N //= i c += 1 factorization.append((i, i**c)) if N != 1: factorization.append((N, N)) return factorization def _modinv(self, a, MOD): r0, r1, s0, s1 = a, MOD, 1, 0 while r1: r0, r1, s0, s1 = r1, r0 % r1, s1, s0-r0//r1*s1 return s0 % MOD m=int(input()) n=int(input()) P=5**8 c=BinomialCoefficient(P) ansP=c(m,n) Q=2**8 c=BinomialCoefficient(Q) ansQ=c(m,n) ans=ansP while ans%Q!=ansQ: ans+=5**8 ans%=10**8 if ans==0: print('0'*8) else: ans=str(ans) print('0'*(8-len(ans))+ans)