結果

問題 No.1039 Project Euler でやれ
ユーザー 37zigen37zigen
提出日時 2020-02-28 18:58:36
言語 Java11
(openjdk 11.0.7)
結果
AC  
実行時間 201 ms / 2,000 ms
コード長 9,061 Byte
コンパイル時間 2,623 ms
使用メモリ 31,864 KB
最終ジャッジ日時 2020-05-30 21:03:32

テストケース

テストケース表示
入力 結果 実行時間
使用メモリ
testcase_00 AC 159 ms
29,484 KB
testcase_01 AC 185 ms
29,832 KB
testcase_02 AC 178 ms
30,124 KB
testcase_03 AC 197 ms
31,704 KB
testcase_04 AC 201 ms
31,864 KB
testcase_05 AC 180 ms
31,680 KB
testcase_06 AC 174 ms
30,156 KB
testcase_07 AC 154 ms
29,468 KB
testcase_08 AC 163 ms
29,472 KB
testcase_09 AC 172 ms
29,976 KB
testcase_10 AC 154 ms
29,432 KB
testcase_11 AC 180 ms
30,280 KB
testcase_12 AC 157 ms
29,464 KB
testcase_13 AC 155 ms
29,440 KB
testcase_14 AC 182 ms
29,848 KB
testcase_15 AC 180 ms
30,168 KB
testcase_16 AC 141 ms
29,396 KB
testcase_17 AC 139 ms
29,440 KB
testcase_18 AC 145 ms
29,432 KB
testcase_19 AC 139 ms
29,388 KB
権限があれば一括ダウンロードができます

ソースコード

diff #
import java.util.Arrays;
import java.util.Scanner;

class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc=new Scanner(System.in);
		int M=sc.nextInt();
		new Main().run(M);
	}
	
	static long MODULO=(long)1e9+7;
	
	long pow(long a,long n) {
		n=(n%(MODULO-1)+(MODULO-1))%(MODULO-1);
		long ret=1;
		for(;n>0;n>>=1,a=a*a%MODULO)if(n%2==1)ret=ret*a%MODULO;
		return ret;
	}
	
	long inv(long a) {
		return pow(a,MODULO-2);
	}
	
	long solve(long p,int e) {
		long[][][] dp=new long[e+1][e+2][e+1];
		dp[0][e+1][0]=1;
		for(int sumKU=0;sumKU<e;++sumKU) {
			for(int k=e+1;k>=1;--k) {
				for(int sumU=0;sumU<e;++sumU) {
					if(dp[sumKU][k][sumU]==0)continue;
					for(int nk=k-1;nk>=1;--nk) {
						for(int nu=1;sumKU+nk*nu<=e;++nu) {
							//(Z/p^nk)^nu
							long add=pow(p,nk*nu*sumU);
							for(int m=0;m<nu;++m) {
								add*=(pow(p,nk*nu)-pow(p,nu*(nk-1)+m))%MODULO*pow(p,nk*sumU)%MODULO;
								add%=MODULO;
							}
							dp[sumKU+nk*nu][nk][sumU+nu]+=inv(add)*dp[sumKU][k][sumU]%MODULO;
							dp[sumKU+nk*nu][nk][sumU+nu]%=MODULO;
						}
					}					
				}
			}
		}
		long ret=0;
		for(int i=1;i<=e;++i)
			for(int j=1;j<=e;++j)
				ret=(ret+dp[e][i][j])%MODULO;
		ret=(ret%MODULO+MODULO)%MODULO;
		return ret;
	}
	
	void run(int M) {
		long fac=factorial(M);
		long ans=1;
		for(long div=2;div<=M;++div) {
			int e=0;
			while(M%div==0) {
				M/=div;
				++e;
			}
			if(e>0) ans=ans*solve(div,e)%MODULO;
		}
		ans=ans*fac%MODULO;
		System.out.println(ans);
	}
	
	// return F^n(0)
	long factorial(long N) {
		build(MODULO);
		long v = (long) Math.sqrt(N);
		int m = 0;
		long[][][] f = new long[m + 1][][];
		for (int i = 0; i <= m; ++i) {
			f[i] = F(m, i * v, N);
		}
		for (int bit = 63; bit >= 0; --bit) {
			if (m > 0) { // m -> 2m
				long[][][] fs = Arrays.copyOfRange(matshift(f, v, m * inv(v, MODULO) % MODULO), m + 1, 2 * m + 2);
				f = matshift(f, v, f.length); // length: m + 1 -> 2m + 2
				fs = matshift(fs, v, fs.length); // length: m + 1 -> 2m + 2
				m *= 2;
				long[][][] f2 = new long[m + 1][][];
				for (int i = 0; i <= m; ++i) {
					f2[i] = matmul(fs[i], f[i]);
				}
				f = f2;
			}
			if (((1L << bit) & v) > 0) { // m -> m + 1
				++m;
				long[][][] f2 = new long[m + 1][][];
				for (int i = 0; i < m; ++i) {
					f2[i] = matmul(f(m, v * i, N), f[i]);
				}
				f2[m] = F(m, m * v, N);
				f = f2;
			}
		}

		long[][] ret = new long[][] { { 1, 0 }, { 0, 1 } };
		for (int i = 0; i <= v - 1; ++i) {
			ret = matmul(f[i], ret);
		}
		for (long i = v * v + 1; i <= N; ++i) {
			ret = matmul(f(i, 0, N), ret);
		}
		return ret[0][0];
	}
	
	long[][] f(long k, long x, long N) {
		long[][] ret = new long[][] { { x+k, 0}, { 0, 0} };
		if (ret[0][1] >= MODULO)
			ret[0][1] -= MODULO;
		if (ret[1][1] >= MODULO)
			ret[1][1] -= MODULO;
		return ret;
	}

	long[][] F(long n, long x, long N) {
		long[][] ret = new long[][] { { 1, 0 }, { 0, 1 } };
		for (int i = 1; i <= n; ++i) {
			ret = matmul(f(i, x, N), ret);
		}
		return ret;
	}

	// m : degree of polynomial
	//
	// Converting
	// from
	// f[0], f[v] , f[2v] , ..., f[mv]
	// to
	// f[0], f[v] , f[2v] , ..., f[mv], f[shift*v], f[shift*v + v] ,f[shift*v + mv]
	// .
	//
	// See f as f(x) = f[x*v].

	long[][][] matshift(long[][][] h, long v, long shift) {
		long[] a0 = new long[h.length];
		for (int i = 0; i < h.length; ++i) {
			a0[i] = h[i][0][0];
		}
		a0 = shift(a0, v, shift);
		long[][][] ret = new long[a0.length][2][2];
		for (int i = 0; i < ret.length; ++i) {
			ret[i] = new long[][] { { a0[i], 0 }, { 0, 0 } };
		}
		return ret;
	}

	long[] shift(long[] h, long v, long shift) {
		int degree = h.length - 1;
		long[] a = new long[degree + 1];
		long[] b = new long[2 * degree + 1];
		long[] ret = new long[2 * h.length];
		for (int i = 0; i < h.length; ++i) {
			ret[i] = h[i];
		}

		long prd = 1;
		for (int i = 0; i <= degree; ++i) {
			a[i] = h[i] * ifac[i] % MODULO * ifac[degree - i] % MODULO * ((degree - i) % 2 == 0 ? 1 : -1);
			if (a[i] < 0)
				a[i] += MODULO;
		}
		for (int i = 0; i <= 2 * degree; ++i)
			b[i] = inv(shift - degree + i, MODULO);
		long[] c = middle_product(a, b, MODULO);
		for (int i = 0; i <= degree; ++i) {
			prd = prd * (shift - i == 0 ? 1 : (shift - i)) % MODULO;
			if (prd < 0)
				prd += MODULO;
		}
		for (int i = 0; i < h.length; ++i) {
			ret[i + h.length] = prd * c[i] % MODULO;
			prd = prd * (shift + i + 1) % MODULO * inv(shift + i - degree, MODULO) % MODULO;
			if (prd < 0)
				prd += MODULO;
		}
		if (0 <= shift && shift <= degree) {
			for (int i = 0; i + shift < h.length; ++i) {
				ret[i + h.length] = h[i + (int) shift];
			}
		}
		return ret;
	}

	long[][] matmul(long[][] a, long[][] b) {
		long[][] ret = new long[a.length][b[0].length];
		for (int i = 0; i < a.length; ++i) {
			for (int j = 0; j < b[i].length; ++j) {
				for (int k = 0; k < a[i].length; ++k) {
					ret[i][j] += a[i][k] * b[k][j] % MODULO;
					if (ret[i][j] >= MODULO)
						ret[i][j] -= MODULO;
				}
			}
		}
		return ret;
	}

	// inv[0] := 1
	long inv(long a, long mod) {
		a %= mod;
		if (a < 0)
			a += mod;
		if (a == 0) {
			throw new AssertionError();
			// return 1;
		}
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		long ret = p < 0 ? (p + mod) : p;
		return ret;
	}

	final int MAX = 112345;
	long[] fac = new long[MAX];
	long[] ifac = new long[MAX];
	long[] inv = new long[MAX];

	void build(long MOD) {
		fac[0] = ifac[0] = inv[0] = fac[1] = ifac[1] = inv[1] = 1;
		for (int i = 2; i < fac.length; ++i) {
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - inv[(int) (MOD % i)] * (MOD / i) % MOD;
			ifac[i] = inv[i] * ifac[i - 1] % MOD;
		}
	}

	long[] middle_product(long[] a, long[] b, long mod0) {
		long[] MOD = new long[] { 1012924417, 1224736769, 1007681537 };
		long[] gen = new long[] { 5, 3, 3 };
		long[][] c = new long[3][];
		for (int i = 0; i < 3; ++i) {
			c[i] = middle_product_(Arrays.copyOf(a, a.length), Arrays.copyOf(b, b.length), MOD[i], gen[i]);
		}
		for (int i = 0; i < c[0].length; ++i) {
			c[0][i] = garner(new long[] { c[0][i], c[1][i], c[2][i] }, MOD, mod0);
		}
		return c[0];
	}

	// a : d 次
	// b : 2d + 1 次
	long[] middle_product_(long[] a, long[] b, long mod, long gen) {
		int degree = a.length - 1;
		{
			int s = 0;
			int t = degree;
			while (s < t) {
				a[s] ^= a[t];
				a[t] ^= a[s];
				a[s] ^= a[t];
				s++;
				t--;
			}
		}
		int level = Long.numberOfTrailingZeros(mod - 1);
		long root = gen;
		long omega = pow(root, (mod - 1) >> level, mod);
		int n = Integer.highestOneBit(2 * degree) << 1;
		long[] roots = new long[level];
		long[] iroots = new long[level];
		roots[0] = omega;
		iroots[0] = inv(omega, mod);
		for (int i = 1; i < level; ++i) {
			roots[i] = roots[i - 1] * roots[i - 1] % mod;
			iroots[i] = iroots[i - 1] * iroots[i - 1] % mod;
		}
		a = Arrays.copyOf(a, n);
		b = Arrays.copyOf(b, n);
		a = fft(a, true, mod, roots, iroots);
		b = fft(b, false, mod, roots, iroots);
		for (int i = 0; i < n; ++i)
			a[i] = a[i] * b[i] % mod;
		a = fft(a, true, mod, roots, iroots);
		long inv = inv(n, mod);
		for (int i = 0; i < n; ++i) {
			a[i] = a[i] * inv % mod;
		}
		return a;
	}

	long[] fft(long[] a, boolean inv, long mod, long[] roots, long[] iroots) {
		int n = a.length;

		int c = 0;
		for (int i = 1; i < n; ++i) {
			for (int j = n >> 1; j > (c ^= j); j >>= 1)
				;
			if (c > i) {
				long d = a[i];
				a[i] = a[c];
				a[c] = d;
			}
		}
		int level = Long.numberOfTrailingZeros(mod - 1);
		for (int i = 1; i < n; i *= 2) {
			long w;
			if (!inv)
				w = roots[level - Integer.numberOfTrailingZeros(i) - 1];
			else
				w = iroots[level - Integer.numberOfTrailingZeros(i) - 1];
			for (int j = 0; j < n; j += 2 * i) {
				long wn = 1;
				for (int k = 0; k < i; ++k) {
					long u = a[j + k];
					long v = a[j + k + i] * wn % mod;
					a[j + k] = u + v;
					a[j + k + i] = u - v;
					if (a[j + k] >= mod)
						a[j + k] -= mod;
					if (a[j + k + i] < 0)
						a[j + k + i] += mod;
					wn = wn * w % mod;
				}
			}
		}
		return a;
	}

	long pow(long a, long n, long mod) {
		long ret = 1;
		for (; n > 0; n >>= 1, a = a * a % mod) {
			if (n % 2 == 1)
				ret = ret * a % mod;
		}
		return ret;
	}

	long garner(long[] x, long[] mod, long mod0) {
		assert x.length == mod.length;
		int n = x.length;
		long[] gamma = new long[n];
		for (int i = 0; i < n; i++) {
			long prod = 1;
			for (int j = 0; j < i; j++) {
				prod = prod * mod[j] % mod[i];
			}
			gamma[i] = inv(prod, mod[i]);
		}
		long[] v = new long[n];
		v[0] = x[0];
		for (int i = 1; i < n; i++) {
			long tmp = v[i - 1];
			for (int j = i - 2; j >= 0; j--) {
				tmp = (tmp * mod[j] + v[j]) % mod[i];
			}
			v[i] = (x[i] - tmp) * gamma[i] % mod[i];
			while (v[i] < 0)
				v[i] += mod[i];
		}
		long ret = 0;
		for (int i = v.length - 1; i >= 0; i--) {
			ret = (ret * mod[i] + v[i]) % mod0;
		}
		return ret;
	}

	
	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
	
}
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