Codeforces 623E Transforming Sequence (分治+FFT)

#include 
#include 
#include 
#include 
using namespace std;


#define N 200020
#define LL long long
#define MOD 1000000007
#define K 3
#define G 3

// 1000000000000000000 30000
int m[] = {1004535809, 998244353, 104857601};

LL qpow(LL x, LL k, int p) {
	LL ret = 1;
	while(k) {
		if(k & 1) ret = ret * x % p;
		k >>= 1;
		x = x * x % p;
	}
	return ret;
}

struct _NTT {
	int p;
	int rev[N];

	void change(LL y[], int len) {
		for(int i = 1; i < len; ++i) {
			rev[i] = (rev[i>>1] >> 1) + ((i & 1) * (len >> 1));
			if(i < rev[i]) swap(y[i], y[rev[i]]);
		}
	}
	void FFT(LL y[], int len, int on) {
		change(y, len);
		for(int h = 2; h <= len; h <<= 1) {
			LL wn = qpow(G, (p - 1) / h, p);
			if(on == -1) wn = qpow(wn, p - 2, p);
			for(int j = 0; j < len; j += h) {
				LL w = 1;
				for(int k = j; k < j + h / 2; ++k) {
					LL u = y[k];
					LL t = w * y[k+h/2] % p;
					y[k] = u + t;
					if(y[k] >= p) y[k] -= p;
					y[k+h/2] = u + p - t;
					if(y[k+h/2] >= p) y[k+h/2] -= p;
					w = w * wn % p;
				}
			}
		}
		if(on == -1) {
			LL inv = qpow(len, p - 2, p);
			for(int i = 0; i < len; ++i) y[i] = y[i] * inv % p;
		}
	}
	void mul(LL a[], LL b[], int len) {
		for(int i = 0; i < len; ++i) {
			a[i] %= p;
			b[i] %= p;
		}
		FFT(a, len, 1);
		FFT(b, len, 1);
		for(int i = 0; i < len; ++i) a[i] = a[i] * b[i] % p;
		FFT(a, len, -1);
	}	
	void debug() {
		LL a[] = {1, 1, 0, 0};
		LL b[] = {1, 1, 0, 0};
		mul(a, b, 4);
		for(int i = 0; i < 4; ++i) printf("%lld ", a[i]);
		puts("");
	}
		
}ntt[K];


LL tmp[N][K], r[K][K];
LL t1[N], t2[N];

LL CRT(LL a[]) {
	LL x[K];
	x[0] = a[0];
	for(int i = 1; i < K; ++i) {
		x[i] = a[i];
		for(int j = 0; j < i; ++j) {
			x[i] = (x[i] - x[j]) % m[i];
			if(x[i] < 0) x[i] += m[i];
			x[i] = x[i] * r[j][i] % m[i];
		}
	}
	LL ret = x[K-1];
	for(int i = K - 2; i >= 0; --i) {
		ret = ret * m[i] % MOD;
		ret = (ret + x[i]) % MOD;
	}
	return ret;
}

void mul(LL a[], LL b[], int len) {
	for(int i = 0; i < K; ++i) {
		for(int j = 0; j < len; ++j) t1[j] = a[j], t2[j] = b[j];
		ntt[i].mul(t1, t2, len);
		for(int j = 0; j < len; ++j) tmp[j][i] = t1[j];
	}
	for(int i = 0; i < len; ++i) a[i] = CRT(tmp[i]);
}

void debug() {
	LL a[] = {1, 1, 0, 0};
	LL b[] = {1, 1, 0, 0};
	mul(a, b, 4);
	for(int i = 0; i < 4; ++i) printf("%lld ", a[i]);
	puts("");
}

int k;
LL dp[N], dp1[N], dp2[N];
LL f[N], nf[N];
int L;

LL C(int n, int m) {
	return f[n] * nf[m] % MOD * nf[n-m] % MOD;
}

void calc(LL n) {
	if(n == 1) {
		for(int i = 1; i <= k; ++i) dp[i] = 1;
		return;
	}
	calc(n / 2);
	for(int i = 0; i < L; ++i) dp1[i] = dp2[i] = 0;

	for(int i = 1; i < k; ++i) {
		dp1[i] = dp[i] * nf[i] % MOD * qpow(2, n / 2 % (MOD - 1) * i, MOD) % MOD;
		dp2[i] = dp[i] * nf[i] % MOD;
	}

	mul(dp1, dp2, L);
	for(int i = 1; i <= k; ++i) dp[i] = dp1[i] * f[i] % MOD;
	if(n & 1) {
		for(int i = 0; i < L; ++i) dp1[i] = dp2[i] = 0;
		for(int i = 1; i <= k; ++i) {
			dp1[i] = dp[i] * nf[i] % MOD * qpow(2, i, MOD) % MOD;
			dp2[i] = nf[i] % MOD;
		}
		mul(dp1, dp2, L);
		for(int i = 1; i <= k; ++i) dp[i] = dp1[i] * f[i] % MOD;
	}
}
		
int main() {
	for(int i = 0; i < K; ++i) {
		ntt[i].p = m[i];
		for(int j = 0; j < i; ++j) r[j][i] = qpow(m[j], m[i] - 2, m[i]);
	}
	nf[0] = f[0] = 1;
	for(int i = 1; i < N; ++i) f[i] = f[i-1] * i % MOD, nf[i] = qpow(f[i], MOD - 2, MOD);

	LL n;
	cin >> n >> k;
	if(n > k) {
		puts("0");
		return 0;
	}
	L = 1;
	while(L <= k * 2) L <<= 1;
	calc(n);
	LL ans = 0;
	for(int i = 1; i <= k; ++i) ans = (ans + dp[i] * C(k, i) % MOD) % MOD;
	cout << ans << endl;
	return 0;
}