結果
| 問題 | No.963 門松列列（2） |
| ユーザー |
 uwi
|
| 提出日時 | 2020-01-06 16:45:30 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 926 ms / 3,000 ms |
| コード長 | 15,730 bytes |
| コンパイル時間 | 5,435 ms |
| コンパイル使用メモリ | 90,024 KB |
| 実行使用メモリ | 73,012 KB |
| 最終ジャッジ日時 | 2024-11-23 00:02:59 |
| 合計ジャッジ時間 | 16,725 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 11 |
ソースコード
package etc;
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 No963 {
InputStream is;
PrintWriter out;
String INPUT = "";
static int mod = 1012924417;
static int G = 5;
void solve()
{
// sec(x) + tan(x) = (1+sin(x))/(cos(x))
int n = ni();
if(n == 1) {
out.println(1);
return;
}
int D = 202030;
long[] num = new long[D+1];
int[][] fif = enumFIF(D+5, mod);
for(int i = 1, s = 1;i <= D;i+=2, s = mod-s) {
num[i] = (long)s * fif[1][i] % mod;
}
num[0]++;
long[] den = new long[D+1];
for(int i = 0, s = 1;i <= D;i+=2, s = mod-s) {
den[i] = (long)s * fif[1][i] % mod;
}
long[] ret = mul(num, inv(den), D+1);
for(int i = 0;i <= D;i++) {
ret[i] = ret[i] * fif[0][i] % mod;
}
out.println(ret[n]*2%mod);
}
public static long[] mul(long[] a, long[] b)
{
return Arrays.copyOf(convoluteSimply(a, b, mod, G), a.length+b.length-1);
}
public static long[] mul(long[] a, long[] b, int lim)
{
return Arrays.copyOf(convoluteSimply(a, b, mod, G), lim);
}
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);
}
// 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;
}
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 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;
}
public 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[] 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 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 No963().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)); }
}