結果
| 問題 | No.963 門松列列（2） |
| ユーザー |
 37zigen
|
| 提出日時 | 2019-12-11 22:42:23 |
| 言語 | Java (openjdk 23) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 19,282 bytes |
| コンパイル時間 | 3,056 ms |
| コンパイル使用メモリ | 92,412 KB |
| 実行使用メモリ | 106,620 KB |
| 最終ジャッジ日時 | 2024-06-25 20:47:42 |
| 合計ジャッジ時間 | 11,909 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | WA * 11 |
ソースコード
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class Main {
InputStream is;
PrintWriter out;
String INPUT = "";
public static int mod = 1000000007;
static int[][] fif = enumFIF(2200005, mod);
void solve() {
int N = ni();
long[] cos0 = new long[N / 2 + 5];
long[] sin0 = new long[N / 2 + 5];
for (int i = 0; i < cos0.length; i++) {
cos0[i] = (long) fif[1][2 * i] * (i % 2 == 0 ? 1 : mod - 1) % mod;
}
for (int i = 0; i < sin0.length; i++) {
sin0[i] = (long) fif[1][2 * i + 1] * (i % 2 == 0 ? 1 : mod - 1) % mod;
}
cos0 = inv(cos0);
sin0 = convolute(sin0, cos0, 3, mod);
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] %= mod;
}
out.println(2 * ret[N] * fif[0][N] % mod);
}
public static long[] mul(long[] a, long[] b) {
if (Math.max(a.length, b.length) >= 3000) {
return Arrays.copyOf(convolute(a, b, 3, mod), a.length + b.length - 1);
} else {
return mulnaive(a, b);
}
}
public static long[] mul(long[] a, long[] b, int lim) {
if (Math.max(a.length, b.length) >= 3000) {
return Arrays.copyOf(convolute(a, b, 3, mod), lim);
} else {
return mulnaive(a, b, lim);
}
}
public static long[] mulnaive(long[] a, long[] b) {
long[] c = new long[a.length + b.length - 1];
long big = 8L * mod * mod;
for (int i = 0; i < a.length; i++) {
for (int j = 0; j < b.length; j++) {
c[i + j] += a[i] * b[j];
if (c[i + j] >= big)
c[i + j] -= big;
}
}
for (int i = 0; i < c.length; i++)
c[i] %= mod;
return c;
}
public static long[] mulnaive(long[] a, long[] b, int lim) {
long[] c = new long[lim];
long big = 8L * mod * mod;
for (int i = 0; i < a.length; i++) {
for (int j = 0; j < b.length && i + j < lim; j++) {
c[i + j] += a[i] * b[j];
if (c[i + j] >= big)
c[i + j] -= big;
}
}
for (int i = 0; i < c.length; i++)
c[i] %= mod;
return c;
}
public static long[] mul_(long[] a, long k) {
for (int i = 0; i < a.length; i++)
a[i] = a[i] * k % mod;
return a;
}
public static long[] mul(long[] a, long k) {
a = Arrays.copyOf(a, a.length);
for (int i = 0; i < a.length; i++)
a[i] = a[i] * k % mod;
return a;
}
public static long[] add(long[] a, long[] b) {
long[] c = new long[Math.max(a.length, b.length)];
for (int i = 0; i < a.length; i++)
c[i] += a[i];
for (int i = 0; i < b.length; i++)
c[i] += b[i];
for (int i = 0; i < c.length; i++)
if (c[i] >= mod)
c[i] -= mod;
return c;
}
public static long[] add(long[] a, long[] b, int lim) {
long[] c = new long[lim];
for (int i = 0; i < a.length && i < lim; i++)
c[i] += a[i];
for (int i = 0; i < b.length && i < lim; i++)
c[i] += b[i];
for (int i = 0; i < c.length; i++)
if (c[i] >= mod)
c[i] -= mod;
return c;
}
public static long[] sub(long[] a, long[] b) {
long[] c = new long[Math.max(a.length, b.length)];
for (int i = 0; i < a.length; i++)
c[i] += a[i];
for (int i = 0; i < b.length; i++)
c[i] -= b[i];
for (int i = 0; i < c.length; i++)
if (c[i] < 0)
c[i] += mod;
return c;
}
public static long[] sub(long[] a, long[] b, int lim) {
long[] c = new long[lim];
for (int i = 0; i < a.length && i < lim; i++)
c[i] += a[i];
for (int i = 0; i < b.length && i < lim; i++)
c[i] -= b[i];
for (int i = 0; i < c.length; i++)
if (c[i] < 0)
c[i] += mod;
return c;
}
// F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x)
// if want p-destructive, comment out flipping p just before returning.
public static long[] inv(long[] p) {
int n = p.length;
long[] f = { invl(p[0], mod) };
for (int i = 0; i < p.length; i++) {
if (p[i] == 0)
continue;
p[i] = mod - p[i];
}
for (int i = 1; i < 2 * n; i *= 2) {
long[] f2 = mul(f, f, Math.min(n, 2 * i));
long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2 * i));
for (int j = 0; j < f.length; j++) {
f2p[j] += 2L * f[j];
if (f2p[j] >= mod)
f2p[j] -= mod;
if (f2p[j] >= mod)
f2p[j] -= mod;
}
f = f2p;
}
for (int i = 0; i < p.length; i++) {
if (p[i] == 0)
continue;
p[i] = mod - p[i];
}
return f;
}
// differentiate
public static long[] d(long[] p) {
long[] q = new long[p.length];
for (int i = 0; i < p.length - 1; i++) {
q[i] = p[i + 1] * (i + 1) % mod;
}
return q;
}
// integrate
public static long[] i(long[] p) {
long[] q = new long[p.length];
for (int i = 0; i < p.length - 1; i++) {
q[i + 1] = p[i] * invl(i + 1, mod) % mod;
}
return q;
}
static long[] exp(long[] a) {
return exp(a, a.length);
}
/**
* https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf
*
* @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series
* @param a
* @param lim
* @return
*/
static long[] exp(long[] a, int lim) {
long[] F = { 1L };
long[] G = { 1L };
long[] da = d(a);
for (int m = 1;; m *= 2) {
long[] G2 = mul(G, G, m);
G = sub(mul_(G, 2), mul(F, G2, m));
long[] Q = Arrays.copyOf(da, m - 1);
long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m - 1)));
F = mul(F, add(new long[] { 1 }, sub(Arrays.copyOf(a, m), i(W))), m);
if (m >= lim)
break;
}
return Arrays.copyOf(F, lim);
}
//
// // F_{t+1}(x) = F_t(x)-(ln F_t(x) - P(x)) * F_t(x)
// public static long[] exp(long[] p)
// {
// int n = p.length;
// long[] f = {p[0]};
// for(int i = 1;i < 2*n;i*=2){
// long[] ii = ln(f);
// long[] sub = sub(ii, p, Math.min(n, 2*i));
// if(--sub[0] < 0)sub[0] += mod;
// for(int j = 0;j < 2*i && j < n;j++){
// sub[j] = mod-sub[j];
// if(sub[j] == mod)sub[j] = 0;
// }
// f = mul(sub, f, Math.min(n, 2*i));
//// f = sub(f, mul(sub(ii, p, 2*i), f, 2*i));
// }
// return f;
// }
// \int f'(x)/f(x) dx
public static long[] ln(long[] f) {
long[] ret = i(mul(d(f), inv(f)));
ret[0] = f[0];
return ret;
}
// ln F(x) - k ln P(x) = 0
public static long[] pow(long[] p, int K) {
int n = p.length;
long[] lnp = ln(p);
for (int i = 1; i < lnp.length; i++)
lnp[i] = lnp[i] * K % mod;
lnp[0] = pow(p[0], K, mod); // go well for some reason
return exp(Arrays.copyOf(lnp, n));
}
// destructive
public static long[] divf(long[] a, int[][] fif) {
for (int i = 0; i < a.length; i++)
a[i] = a[i] * fif[1][i] % mod;
return a;
}
// destructive
public static long[] mulf(long[] a, int[][] fif) {
for (int i = 0; i < a.length; i++)
a[i] = a[i] * fif[0][i] % mod;
return a;
}
public static long[] transformExponentially(long[] a, int[][] fif) {
return mulf(exp(divf(Arrays.copyOf(a, a.length), fif)), fif);
}
public static long[] transformLogarithmically(long[] a, int[][] fif) {
return mulf(Arrays.copyOf(ln(divf(Arrays.copyOf(a, a.length), fif)), a.length), fif);
}
// 1/(1-F)-1
static long[] transformInvertly(long[] a) {
long[] b = new long[a.length];
for (int i = 0; i < a.length; i++) {
b[i] = mod - a[i];
if (b[i] == mod)
b[i] = 0;
}
if (++b[0] == mod)
b[0] = 0;
long[] ret = inv(b);
if (--ret[0] < 0)
ret[0] += mod;
return ret;
}
// -1/(1+F)+1
static long[] transformInverseOfInvertly(long[] a) {
long[] b = new long[a.length];
for (int i = 0; i < a.length; i++) {
b[i] = a[i];
}
if (++b[0] == mod)
b[0] = 0;
long[] ret = inv(b);
for (int i = 0; i < a.length; i++) {
ret[i] = mod - ret[i];
if (ret[i] == mod)
ret[i] = 0;
}
if (++ret[0] == mod)
ret[0] = 0;
return ret;
}
public static long[] reverse(long[] p) {
long[] ret = new long[p.length];
for (int i = 0; i < p.length; i++) {
ret[i] = p[p.length - 1 - i];
}
return ret;
}
public static long[] reverse(long[] p, int lim) {
long[] ret = new long[lim];
for (int i = 0; i < lim && i < p.length; i++) {
ret[i] = p[p.length - 1 - i];
}
return ret;
}
// [quotient, remainder]
// remainder can be empty.
//
// deg(f)=n, deg(g)=m, f=gq+r, f=gq+r.
// f* = x^n*f(1/x),
// t=g*^-1 mod x^(n-m+1), q=(tf* mod x^(n-m+1))*
public static long[][] div(long[] f, long[] g) {
int n = f.length, m = g.length;
if (n < m)
return new long[][] { new long[0], Arrays.copyOf(f, n) };
long[] rf = reverse(f, n - m + 1);
long[] rg = reverse(g, n - m + 1);
long[] rq = mul(rf, inv(rg), n - m + 1);
long[] q = reverse(rq, n - m + 1);
long[] r = sub(f, mul(q, g, m - 1), m - 1);
return new long[][] { q, r };
}
// public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
// public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};
public static final int[] NTTPrimes = { 1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769,
950009857, 943718401, 935329793, 924844033 };
public static final int[] NTTPrimitiveRoots = { 5, 3, 3, 3, 17, 7, 7, 7, 3, 5 };
public static long[] convoluteSimply(long[] a, long[] b, int P, int g) {
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for (int i = 0; i < m; i++) {
fa[i] = fa[i] * fb[i] % P;
}
return nttmb(fa, m, true, P, g);
}
public static long[] convolute(long[] a, long[] b) {
int USE = 2;
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
long[][] fs = new long[USE][];
for (int k = 0; k < USE; k++) {
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for (int i = 0; i < m; i++) {
fa[i] = fa[i] * fb[i] % P;
}
fs[k] = nttmb(fa, m, true, P, g);
}
int[] mods = Arrays.copyOf(NTTPrimes, USE);
long[] gammas = garnerPrepare(mods);
int[] buf = new int[USE];
for (int i = 0; i < fs[0].length; i++) {
for (int j = 0; j < USE; j++)
buf[j] = (int) fs[j][i];
long[] res = garnerBatch(buf, mods, gammas);
long ret = 0;
for (int j = res.length - 1; j >= 0; j--)
ret = ret * mods[j] + res[j];
fs[0][i] = ret;
}
return fs[0];
}
public static long[] convolute(long[] a, long[] b, int USE, int mod) {
int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2);
long[][] fs = new long[USE][];
for (int k = 0; k < USE; k++) {
int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
long[] fa = nttmb(a, m, false, P, g);
long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
for (int i = 0; i < m; i++) {
fa[i] = fa[i] * fb[i] % P;
}
fs[k] = nttmb(fa, m, true, P, g);
}
int[] mods = Arrays.copyOf(NTTPrimes, USE);
long[] gammas = garnerPrepare(mods);
int[] buf = new int[USE];
for (int i = 0; i < fs[0].length; i++) {
for (int j = 0; j < USE; j++)
buf[j] = (int) fs[j][i];
long[] res = garnerBatch(buf, mods, gammas);
long ret = 0;
for (int j = res.length - 1; j >= 0; j--)
ret = (ret * mods[j] + res[j]) % mod;
fs[0][i] = ret;
}
return fs[0];
}
// static int[] wws = new int[270000]; // outer faster
// Modifed Montgomery + Barrett
private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) {
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P) << 1;
int H = Long.numberOfTrailingZeros(K) * 2;
long M = K * K / P;
int[] wws = new int[1 << h - 1];
long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P);
long w = (1L << 32) % P;
for (int k = 0; k < 1 << h - 1; k++) {
wws[k] = (int) w;
w = modh(w * dw, M, H, P);
}
long J = invl(P, 1L << 32);
for (int i = 0; i < h; i++) {
for (int j = 0; j < 1 << i; j++) {
for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++, s++, t++) {
long u = (dst[s] - dst[t] + 2 * P) * wws[k];
dst[s] += dst[t];
if (dst[s] >= 2 * P)
dst[s] -= 2 * P;
// long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
long Q = (u << 32) * J >>> 32;
dst[t] = (u >>> 32) - (Q * P >>> 32) + P;
}
}
if (i < h - 1) {
for (int k = 0; k < 1 << h - i - 2; k++)
wws[k] = wws[k * 2];
}
}
for (int i = 0; i < n; i++) {
if (dst[i] >= P)
dst[i] -= P;
}
for (int i = 0; i < n; i++) {
int rev = Integer.reverse(i) >>> -h;
if (i < rev) {
long d = dst[i];
dst[i] = dst[rev];
dst[rev] = d;
}
}
if (inverse) {
long in = invl(n, P);
for (int i = 0; i < n; i++)
dst[i] = modh(dst[i] * in, M, H, P);
}
return dst;
}
// Modified Shoup + Barrett
private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) {
long[] dst = Arrays.copyOf(src, n);
int h = Integer.numberOfTrailingZeros(n);
long K = Integer.highestOneBit(P) << 1;
int H = Long.numberOfTrailingZeros(K) * 2;
long M = K * K / P;
long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P);
long[] wws = new long[1 << h - 1];
long[] ws = new long[1 << h - 1];
long w = 1;
for (int k = 0; k < 1 << h - 1; k++) {
wws[k] = (w << 32) / P;
ws[k] = w;
w = modh(w * dw, M, H, P);
}
for (int i = 0; i < h; i++) {
for (int j = 0; j < 1 << i; j++) {
for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++, s++, t++) {
long ndsts = dst[s] + dst[t];
if (ndsts >= 2 * P)
ndsts -= 2 * P;
long T = dst[s] - dst[t] + 2 * P;
long Q = wws[k] * T >>> 32;
dst[s] = ndsts;
dst[t] = ws[k] * T - Q * P & (1L << 32) - 1;
}
}
// dw = dw * dw % P;
if (i < h - 1) {
for (int k = 0; k < 1 << h - i - 2; k++) {
wws[k] = wws[k * 2];
ws[k] = ws[k * 2];
}
}
}
for (int i = 0; i < n; i++) {
if (dst[i] >= P)
dst[i] -= P;
}
for (int i = 0; i < n; i++) {
int rev = Integer.reverse(i) >>> -h;
if (i < rev) {
long d = dst[i];
dst[i] = dst[rev];
dst[rev] = d;
}
}
if (inverse) {
long in = invl(n, P);
for (int i = 0; i < n; i++) {
dst[i] = modh(dst[i] * in, M, H, P);
}
}
return dst;
}
static final long mask = (1L << 31) - 1;
public static long modh(long a, long M, int h, int mod) {
long r = a - ((M * (a & mask) >>> 31) + M * (a >>> 31) >>> h - 31) * mod;
return r < mod ? r : r - mod;
}
private static long[] garnerPrepare(int[] m) {
int n = m.length;
assert n == m.length;
if (n == 0)
return new long[0];
long[] gamma = new long[n];
for (int k = 1; k < n; k++) {
long prod = 1;
for (int i = 0; i < k; i++) {
prod = prod * m[i] % m[k];
}
gamma[k] = invl(prod, m[k]);
}
return gamma;
}
private static long[] garnerBatch(int[] u, int[] m, long[] gamma) {
int n = u.length;
assert n == m.length;
long[] v = new long[n];
v[0] = u[0];
for (int k = 1; k < n; k++) {
long temp = v[k - 1];
for (int j = k - 2; j >= 0; j--) {
temp = (temp * m[j] + v[j]) % m[k];
}
v[k] = (u[k] - temp) * gamma[k] % m[k];
if (v[k] < 0)
v[k] += m[k];
}
return v;
}
private static long pow(long a, long n, long mod) {
// a %= mod;
long ret = 1;
int x = 63 - Long.numberOfLeadingZeros(n);
for (; x >= 0; x--) {
ret = ret * ret % mod;
if (n << 63 - x < 0)
ret = ret * a % mod;
}
return ret;
}
private static long invl(long a, long mod) {
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;
}
return p < 0 ? p + mod : p;
}
public static long C(int n, int r, int mod, int[][] fif) {
if (n < 0 || r < 0 || r > n)
return 0;
return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
}
public static int[][] enumFIF(int n, int mod) {
int[] f = new int[n + 1];
int[] invf = new int[n + 1];
f[0] = 1;
for (int i = 1; i <= n; i++) {
f[i] = (int) ((long) f[i - 1] * i % mod);
}
long a = f[n];
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;
}
invf[n] = (int) (p < 0 ? p + mod : p);
for (int i = n - 1; i >= 0; i--) {
invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
}
return new int[][] { f, invf };
}
void run() throws Exception {
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if (!INPUT.isEmpty())
tr(System.currentTimeMillis() - s + "ms");
// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
// @Override
// public void run() {
// long s = System.currentTimeMillis();
// solve();
// out.flush();
// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// }
// };
// t.start();
// t.join();
}
public static void main(String[] args) throws Exception {
new Main().run();
}
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
private int readByte() {
if (lenbuf == -1)
throw new InputMismatchException();
if (ptrbuf >= lenbuf) {
ptrbuf = 0;
try {
lenbuf = is.read(inbuf);
} catch (IOException e) {
throw new InputMismatchException();
}
if (lenbuf <= 0)
return -1;
}
return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) {
return !(c >= 33 && c <= 126);
}
private int skip() {
int b;
while ((b = readByte()) != -1 && isSpaceChar(b))
;
return b;
}
private double nd() {
return Double.parseDouble(ns());
}
private char nc() {
return (char) skip();
}
private String ns() {
int b = skip();
StringBuilder sb = new StringBuilder();
while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n) {
char[] buf = new char[n];
int b = skip(), p = 0;
while (p < n && !(isSpaceChar(b))) {
buf[p++] = (char) b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private int[] na(int n) {
int[] a = new int[n];
for (int i = 0; i < n; i++)
a[i] = ni();
return a;
}
private long[] nal(int n) {
long[] a = new long[n];
for (int i = 0; i < n; i++)
a[i] = nl();
return a;
}
private char[][] nm(int n, int m) {
char[][] map = new char[n][];
for (int i = 0; i < n; i++)
map[i] = ns(m);
return map;
}
private int[][] nmi(int n, int m) {
int[][] map = new int[n][];
for (int i = 0; i < n; i++)
map[i] = na(m);
return map;
}
private int ni() {
return (int) nl();
}
private long nl() {
long num = 0;
int b;
boolean minus = false;
while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
;
if (b == '-') {
minus = true;
b = readByte();
}
while (true) {
if (b >= '0' && b <= '9') {
num = num * 10 + (b - '0');
} else {
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) {
System.out.println(Arrays.deepToString(o));
}
}