結果
| 問題 | No.502 階乗を計算するだけ |
| コンテスト | |
| ユーザー |
 uwi
|
| 提出日時 | 2017-04-08 15:50:35 |
| 言語 | Java (openjdk 23) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 18,414 bytes |
| 記録 | |
| コンパイル時間 | 5,203 ms |
| コンパイル使用メモリ | 90,552 KB |
| 実行使用メモリ | 77,792 KB |
| 最終ジャッジ日時 | 2024-07-17 23:49:49 |
| 合計ジャッジ時間 | 15,192 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 44 WA * 2 TLE * 6 |
ソースコード
package contest;
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 Factorial {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
int mod = 1000000007;
long nlong = nl();
if(nlong >= mod){
out.println(0);
return;
}
if(nlong == 0){
out.println(1);
return;
}
superPrepare();
int n = (int)nlong;
boolean inv = false;
if(n > mod-n){
n = mod - n;
inv = true;
}
int s = (int)Math.sqrt(n);
long[] vs = new long[n/s];
for(int i = 0;i < n/s;i++){
vs[i] = 1 + i * s;
}
long[] f = buildProductPlus(vs);
long[] cs = new long[s];
for(int i = 0;i < s;i++)cs[i] = i;
long[] res = substitute(f, cs);
long ret = 1;
for(long v : res)ret = ret * v % mod;
for(int i = s*(n/s)+1;i <= n;i++){
ret = ret * i % mod;
}
if(inv){
ret = mod-invl(ret, mod);
}
out.println(ret);
}
public static long[] buildProductPlus(long[] vs)
{
return dfsBPP(0, vs.length, vs);
}
private static long[] dfsBPP(int l, int r, long[] vs)
{
if(r-l == 1){
return new long[]{vs[l], 1};
}else{
int h = l+r>>1;
return mul(dfsBPP(l, h, vs), dfsBPP(h, r, vs));
}
}
public static int mod = 1000000007;
public static long[] mul(long[] a, long[] b)
{
if(Math.max(a.length, b.length) >= 1500){
return Arrays.copyOf(convolute3(a, b, mod, null), 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) >= 1500){
return Arrays.copyOf(convolute3(a, b, mod, null), 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[] 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;
}
// 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;
}
// 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);
}
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.
// @see http://www.dis.uniroma1.it/~sankowski/lecture4.pdf
public static long[][] div(long[] p, long[] q)
{
if(p.length < q.length)return new long[][]{new long[0], Arrays.copyOf(p, p.length)};
long[] rp = reverse(p, p.length-q.length+1);
long[] rq = reverse(q, p.length-q.length+1);
long[] rd = mul(rp, inv(rq), p.length-q.length+1);
long[] d = reverse(rd, p.length-q.length+1);
long[] r = sub(p, mul(d, q, q.length-1), q.length-1);
return new long[][]{d, r};
}
public static long[] substitute(long[] p, long[] xs)
{
return descendProductTree(p, buildProductTree(xs));
}
public static long[][] buildProductTree(long[] xs)
{
int m = Integer.highestOneBit(xs.length)*4;
long[][] ms = new long[m][];
for(int i = 0;i < xs.length;i++){
ms[m/2+i] = new long[]{mod-xs[i], 1};
}
for(int i = m/2-1;i >= 1;i--){
if(ms[2*i] == null){
ms[i] = null;
}else if(ms[2*i+1] == null){
ms[i] = ms[2*i];
}else{
ms[i] = mul(ms[2*i], ms[2*i+1]);
}
}
return ms;
}
public static long[] descendProductTree(long[] p, long[][] pt)
{
long[] rets = new long[pt[1].length-1];
dfs(p, pt, 1, rets);
return rets;
}
private static void dfs(long[] p, long[][] pt, int cur, long[] rets)
{
if(pt[cur] == null)return;
if(cur >= pt.length/2){
rets[cur-pt.length/2] = p[0];
}else{
// F = q1X+r1
// F = q2Y+r2
if(p.length >= 200){
if(pt[2*cur+1] != null){
long[][] qr0 = div(p, pt[2*cur]);
dfs(qr0[1], pt, cur*2, rets);
long[][] qr1 = div(p, pt[2*cur+1]);
dfs(qr1[1], pt, cur*2+1, rets);
}else if(pt[2*cur] != null){
long[] nex = cur == 1 ? div(p, pt[2*cur])[1] : p;
dfs(nex, pt, cur*2, rets);
}
}else{
if(pt[2*cur+1] != null){
dfs(modnaive(p, pt[2*cur]), pt, cur*2, rets);
dfs(modnaive(p, pt[2*cur+1]), pt, cur*2+1, rets);
}else if(pt[2*cur] != null){
long[] nex = cur == 1 ? modnaive(p, pt[2*cur]) : p;
dfs(nex, pt, cur*2, rets);
}
}
}
}
public static long[][] divnaive(long[] a, long[] b)
{
int n = a.length, m = b.length;
if(n-m+1 <= 0)return new long[][]{new long[0], Arrays.copyOf(a, n)};
long[] r = Arrays.copyOf(a, n);
long[] q = new long[n-m+1];
long ib = invl(b[m-1], mod);
for(int i = n-1;i >= m-1;i--){
long x = ib * r[i] % mod;
q[i-(m-1)] = x;
for(int j = m-1;j >= 0;j--){
r[i+j-(m-1)] -= b[j]*x;
r[i+j-(m-1)] %= mod;
if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;
// r[i+j-(m-1)] = modh(r[i+j-(m-1)]+(long)mod*mod - b[j]*x, MM, HH, mod);
}
}
return new long[][]{q, Arrays.copyOf(r, m-1)};
}
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 long[] convolute(long[] a, long[] b)
// {
// int USE = 2;
// int m = Math.max(2, Integer.highestOneBit(a.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];
// }
static int L = 16; // max m = 2^L
static long[][] cache = new long[6][1<<L];
// using cache, optimize memory.
public static long[] convolute3(long[] a, long[] b, int mod, long[][] ffb)
{
int m = ffb != null ? ffb[0].length : Math.max(2, Integer.highestOneBit(a.length+b.length-1)<<1);
long[][] fs = new long[3][];
for(int k = 0;k < 3;k++){
int P = NTTPrimes[k];
long[] fa = nttmb(a, m, false, cache[k*2], k);
long[] fb = ffb != null ? ffb[k] : a == b ? fa : nttmb(b, m, false, cache[k*2+1], k);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
fs[k] = nttmb(fa, m, true, k);
}
// mods={1053818881, 1051721729, 1045430273
// gamma=[[0, 525860363, 152479290]]
long F = 1051721729L * 1053818881L % mod;
long[] res = new long[a.length+b.length-1];
for(int i = 0;i < res.length;i++){
long v0 = fs[0][i];
long v1 = (fs[1][i] - v0 + 1051721729L + 1051721729L) * 525860363L % 1051721729L;
long v2 = ((fs[2][i] - v0 + 1045430273L) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L;
long ret = (v2 * F + v1 * 1053818881L + v0) % mod;
res[i] = ret;
}
return res;
}
// if m is not max size, not using cache will be faster.
public static long[] convolute3NoCache(long[] a, long[] b, int mod, long[][] ffb)
{
int m = ffb != null ? ffb[0].length : Math.max(2, Integer.highestOneBit(a.length+b.length-1)<<1);
long[][] fs = new long[3][];
for(int k = 0;k < 3;k++){
int P = NTTPrimes[k];
long[] fa = nttmb(a, m, false, null, k);
long[] fb = ffb != null ? ffb[k] : a == b ? fa : nttmb(b, m, false, null, k);
for(int i = 0;i < m;i++){
fa[i] = fa[i]*fb[i]%P;
}
fs[k] = nttmb(fa, m, true, k);
}
// mods={1053818881, 1051721729, 1045430273
// gamma=[[0, 525860363, 152479290]]
long F = 1051721729L * 1053818881L % mod;
long[] res = new long[a.length+b.length-1];
for(int i = 0;i < res.length;i++){
long v0 = fs[0][i];
long v1 = (fs[1][i] - v0 + 1051721729L + 1051721729L) * 525860363L % 1051721729L;
long v2 = ((fs[2][i] - v0 + 1045430273L) * 152479290L + v1 * (1045430273L-871191728L)) % 1045430273L;
long ret = (v2 * F + v1 * 1053818881L + v0) % mod;
res[i] = ret;
}
return res;
}
static int[][][] wws;
static int[][][] iwws;
static void superPrepare()
{
wws = new int[3][][];
iwws = new int[3][][];
for(int t = 0;t < 3;t++){
int P = NTTPrimes[t], g = NTTPrimitiveRoots[t];
long K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
{
wws[t] = new int[L+1][];
long w = (1L<<32)%P;
long dw = pow(g, P-1>>>L, P);
wws[t][L] = new int[1<<L-1];
for(int k = 0;k < 1<<L-1;k++){
wws[t][L][k] = (int)w;
w = modh(w*dw, M, H, P);
}
for(int i = L-1;i >= 1;i--){
wws[t][i] = new int[1<<i-1];
for(int k = 0;k < 1<<i-1;k++)wws[t][i][k] = wws[t][i+1][k*2];
}
}
{
iwws[t] = new int[L+1][];
long w = (1L<<32)%P;
long dw = pow(g, P-1-(P-1>>>L), P);
iwws[t][L] = new int[1<<L-1];
for(int k = 0;k < 1<<L-1;k++){
iwws[t][L][k] = (int)w;
w = modh(w*dw, M, H, P);
}
for(int i = L-1;i >= 1;i--){
iwws[t][i] = new int[1<<i-1];
for(int k = 0;k < 1<<i-1;k++)iwws[t][i][k] = iwws[t][i+1][k*2];
}
}
}
}
private static long[] nttmb(long[] src, int n, boolean inverse, int ind){
return nttmb(src, n, inverse, new long[n], ind);
}
// Modifed Montgomery + Barrett
private static long[] nttmb(long[] src, int n, boolean inverse, long[] dst, int ind)
{
int P = NTTPrimes[ind];
System.arraycopy(src, 0, dst, 0, Math.min(n, src.length));
Arrays.fill(dst, Math.min(n, src.length), n, 0);
int h = Integer.numberOfTrailingZeros(n);
long J = invl(P, 1L<<32);
int[][] mul = inverse ? iwws[ind] : wws[ind];
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)*mul[h-i][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;
}
}
}
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 K = Integer.highestOneBit(P)<<1;
int H = Long.numberOfTrailingZeros(K)*2;
long M = K*K/P;
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;
}
public static long[] modnaive(long[] a, long[] b)
{
int n = a.length, m = b.length;
if(n-m+1 <= 0)return a;
long[] r = Arrays.copyOf(a, n);
long ib = invl(b[m-1], mod);
for(int i = n-1;i >= m-1;i--){
long x = ib * r[i] % mod;
for(int j = m-1;j >= 0;j--){
r[i+j-(m-1)] -= b[j]*x;
r[i+j-(m-1)] %= mod;
if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;
// r[i+j-(m-1)] = modh(r[i+j-(m-1)]+(long)mod*mod - b[j]*x, MM, HH, mod);
}
}
return Arrays.copyOf(r, m-1);
}
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 Factorial().run(); }
private byte[] inbuf = new byte[1024];
private 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)); }
}