結果

問題 No.963 門松列列(2)
ユーザー 37zigen
提出日時 2019-12-11 21:48:33
言語 Java11
(openjdk 11.0.5)
結果
WA   .
実行時間 -
コード長 6,286 Byte
コンパイル時間 2,564 ms
使用メモリ 204,776 KB
最終ジャッジ日時 2020-01-17 22:13:15

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
00small1.txt WA -
00small2.txt WA -
00small3.txt WA -
00small4.txt WA -
00small5.txt WA -
rnd1.txt TLE -
rnd2.txt WA -
rnd3.txt TLE -
rnd4.txt TLE -
rnd5.txt -- -
xyz_largest.txt -- -
テストケース一括ダウンロード

ソースコード

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

class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	int MAX = 3123456;

	long[] fac = new long[MAX];
	long[] ifac = new long[MAX];
	long[] inv = new long[MAX];
	long[] pw2 = new long[MAX];

	{
		long MOD = (long) 1e9 + 7;
		fac[0] = fac[1] = ifac[0] = ifac[1] = inv[0] = inv[1] = pw2[0] = 1;
		pw2[1] = 2;
		for (int i = 2; i < fac.length; ++i) {
			fac[i] = i * fac[i - 1] % MOD;
			inv[i] = MOD - inv[(int) (MOD % i)] * (MOD / i) % MOD;
			ifac[i] = inv[i] * ifac[i - 1] % MOD;
			pw2[i] = 2 * pw2[i - 1] % MOD;
		}
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		//long curTime=System.currentTimeMillis();
		//for(int N=202020;N<=202020;++N)
		System.out.println(solve(N, (long) 1e9 + 7));
		//System.out.println(System.currentTimeMillis()-curTime);
	}

	long comb(int n, int k, long mod) {
		return fac[n] * ifac[k] % mod * ifac[n - k] % mod;
	}

	long solve(int N, long mod0) {
		long[] cos0=new long[N/2+5];
		long[] sin0=new long[N/2+5];
		for(int i=0;i<cos0.length;i++){
			cos0[i]=ifac[2*i]*(i%2==0?1:mod0-1)%mod0;
		}
		//cos[2*i]=cos0[i]
		for(int i=0;i<sin0.length;i++){
			sin0[i]=ifac[2*i+1]*(i%2==0?1:mod0-1)%mod0;
		}
		//sin[2*i+1]=sin0[i]
		cos0=inv(cos0,mod0);
		sin0=mul(sin0,cos0,mod0);//xf(x^2)g(x^2)
		long[] ret=new long[N+1];
		for(int i=0;i<sin0.length&&2*i+1<ret.length;++i){
			ret[2*i+1]=sin0[i];
		}
		for(int i=0;i<cos0.length&&2*i<ret.length;++i){
			ret[2*i]+=cos0[i];
			ret[2*i]%=mod0;
		}
		return 2*ret[N]*fac[N]%mod0;
	}
    
    long[] inv(long[] F, long mod0) {
        long[] G = new long[1];
        G[0] = 1;
        while (G.length < F.length) {
            int len = G.length;
            G = subtract(mul(G, 2, mod0), mul(Arrays.copyOf(F, 2 * len), mul(G, G, mod0), mod0), mod0);
            G = Arrays.copyOf(G, 2 * len);
        }
        return G;
    }
    
    long[] mul(long[] a, long coe, long mod0) {
        long[] ret = new long[a.length];
        for (int i = 0; i < ret.length; ++i) {
            ret[i] = coe * a[i] % mod0;
        }
        return ret;
    }
    
    long[] subtract(long[] a, long[] b, long mod0) {
        long[] ret = new long[Math.max(a.length, b.length)];
        for (int i = 0; i < ret.length; ++i) {
            ret[i] = (i < a.length ? a[i] : 0) - (i < b.length ? b[i] : 0);
            ret[i] = (ret[i] + mod0) % mod0;
        }
        return ret;
    }

	long[] mul(long[] a, long[] b, long mod0) {
		if (a.length == 1) {
			long[] ret = new long[b.length];
			for (int i = 0; i < b.length; ++i) {
				ret[i] = a[0] * b[i] % mod0;
			}
			return ret;
		} else if (b.length == 1) {
			long[] ret = new long[a.length];
			for (int i = 0; i < a.length; ++i) {
				ret[i] = a[i] * b[0] % mod0;
			}
			return ret;
		}
		// 2^25*5+1, 2^24*73+1, 2^26*7+1
		long[] MOD = new long[] { 167772161, 1224736769, 469762049 };
		long[] gen = new long[] { 3, 3, 3 };
		long[][] c = new long[3][];
		for (int i = 0; i < 3; ++i) {
			c[i] = mul(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];
	}

	long[] mul(long[] a, long[] b, long mod, long gen) {
		int degree = Math.max(a.length - 1, b.length - 1);
		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, false, 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 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;
	}

	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;
	}

	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;
	}

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

}
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