結果
| 問題 |
No.2181 LRM Question 2
|
| コンテスト | |
| ユーザー |
 uwi
|
| 提出日時 | 2023-01-06 22:58:43 |
| 言語 | Java (openjdk 23) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 19,173 bytes |
| コンパイル時間 | 6,557 ms |
| コンパイル使用メモリ | 93,656 KB |
| 実行使用メモリ | 159,508 KB |
| 最終ジャッジ日時 | 2024-11-30 19:34:24 |
| 合計ジャッジ時間 | 25,729 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 18 TLE * 5 |
ソースコード
package contest230106;
import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class G {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
long L = nl(), R = nl();
int mod = ni();
// i < mod and n-(i+1) < modのときだけ非0
// i+1 > n-mod
// n-mod-1 < i < mod
// n-mod < mod
// n < 2*mod
// n^2*(n-1)^2*..*(n-i+1)^2 * (i+1)^2*...*n^2
// -------------------------------------------
// 1^2*2^2*...n^2
// n^2*(n-1)^2*..*(n-i+1)^2
// -------------------------------------------
// 1^2*2^2*...i^2
// C(n,i)^2
// sum_n sum_{i=1}^{n-1} C(n,i)^2 = (2n)!/(n!)^2-2
// (2n)(2n-1)(2n-2)...(n+1)
// -------------------------
// n..........1
int[] primes = sieveEratosthenes(1000);
int[][] F = factor(mod, primes);
long ans = -2*(R-L+1);
for(int i = 0;i < R-L+1;i++){
long n = L+i;
long gmod = 1;
long gval = 0;
for(int[] item : F){
long val = C(2*n, n, item[0], item[1]);
long mo = 1;
for(int j = 0;j < item[1];j++){
mo = mo * item[0];
}
gval = crt(gmod, gval, mo, val);
gmod *= mo;
}
ans += gval;
}
ans %= mod;
if(ans < 0)ans += mod;
out.println(ans);
}
public static int[][] factor(int n, int[] primes)
{
int[][] ret = new int[9][2];
int rp = 0;
for(int p : primes){
if(p * p > n)break;
int i;
for(i = 0;n % p == 0;n /= p, i++);
if(i > 0){
ret[rp][0] = p;
ret[rp][1] = i;
rp++;
}
}
if(n != 1){
ret[rp][0] = n;
ret[rp][1] = 1;
rp++;
}
return Arrays.copyOf(ret, rp);
}
public static long crt(long p, long m, long q, long n)
{
assert p > 0;
assert q > 0;
assert 0 <= m;
assert m < p;
assert 0 <= n;
assert n < q;
if(p < q)return crt(q, n, p, m);
long a = p, b = q;
long pp = 1, qq = 0;
while(b > 0){
long c = a / b;
long d;
d = a; a = b; b = d % b;
d = pp; pp = qq; qq = d - c * qq;
}
if((n - m) % a != 0)return -1;
long mod = p / a * q;
// long ret = (p * pp % mod * ((n - m) / a) + m) % mod;
long ret = ((n-m)*pp%q) * (p/a) + m;
if(ret < 0)ret += mod;
return ret;
}
public static int[] sieveEratosthenes(int n) {
if (n <= 32) {
int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
for (int i = 0; i < primes.length; i++) {
if (n < primes[i]) {
return Arrays.copyOf(primes, i);
}
}
return primes;
}
int u = n + 32;
double lu = Math.log(u);
int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
ret[0] = 2;
int pos = 1;
int[] isnp = new int[(n + 1) / 32 / 2 + 1];
int sup = (n + 1) / 32 / 2 + 1;
int[] tprimes = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
for (int tp : tprimes) {
ret[pos++] = tp;
int[] ptn = new int[tp];
for (int i = (tp - 3) / 2; i < tp << 5; i += tp) ptn[i >> 5] |= 1 << (i & 31);
for (int j = 0; j < sup; j += tp) {
for (int i = 0; i < tp && i + j < sup; i++) {
isnp[j + i] |= ptn[i];
}
}
}
// 3,5,7
// 2x+3=n
int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14};
int h = n / 2;
for (int i = 0; i < sup; i++) {
for (int j = ~isnp[i]; j != 0; j &= j - 1) {
int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
int p = 2 * pp + 3;
if (p > n) break;
ret[pos++] = p;
if ((long) p * p > n) continue;
for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q;
}
}
return Arrays.copyOf(ret, pos);
}
public static long C(long n, long r, int p, int q)
{
if(r < 0 || r > n)return 0;
long P = 1;
for(int i = 0;i < q;i++)P *= p;
long z = n - r;
long e0 = 0;
for(long u = n/p;u > 0;u /= p)e0 += u;
for(long u = r/p;u > 0;u /= p)e0 -= u;
for(long u = z/p;u > 0;u /= p)e0 -= u;
if(e0 >= q)return 0;
// long em = 0;
// for(long u = n/P*p;u > 0;u /= p)em += u;
// for(long u = r/P*p;u > 0;u /= p)em -= u;
// for(long u = z/P*p;u > 0;u /= p)em -= u;
long[] fact = new long[p*(q+1)+1];
long[] ifact = new long[p*(q+1)+1];
fact[0] = ifact[0] = 1;
for(int i = 1;i <= p*(q+1);i++){
if(i % p == 0){
fact[i] = fact[i-1];
}else{
fact[i] = mul(fact[i-1], i, P);
}
ifact[i] = invl(fact[i], P);
}
long ret = 1;
while(n > 0){
ret = mul(mul(mul(
ret, ff(n, p, q, fact, ifact), P),
invl(ff(r, p, q, fact, ifact), P), P),
invl(ff(z, p, q, fact, ifact), P), P)
;
n /= p; r /= p; z /= p;
}
ret = mul(ret, pow(p, e0, P), P);
// if(!(p == 2 && q >= 3) && (em&1)==1){
// tr("kimasi");
// ret = (P-ret) % P;
// }
return ret;
}
public static long ff(long n, int p, int q, long[] fact, long[] ifact)
{
long u = n/p;
int v = (int)(n%p);
boolean plused = q % 2 == 0;
if(plused)q++;
int r = (q-1)/2;
long P = 1;
for(int j = 1;j <= q;j++)P *= p;
long PP = P / p * (p-1);
// tr(n, p, q, u, v, r, P, PP);
long ret = fact[v];
outer:
for(int j = 1;j <= r;j++){
long[] betanums = new long[2*r+1];
long sign = 1;
for(int i = -r;i <= r;i++){
if(i != j && -i != j){
if(u-i == 0)continue outer;
betanums[i+r] = u-i;
if(betanums[i+r] < 0){
sign *= -1;
betanums[i+r] *= -1;
}
}
}
for(int i = -r;i <= r;i++){
if(i != j && -i != j){
long w = j-i;
if(w < 0){
sign *= -1;
w *= -1;
}
for(int k = 0;k <= 2*r;k++){
if(betanums[k] != 0){
long g = gcd(betanums[k], w);
betanums[k] /= g;
w /= g;
}
}
if(w != 1){
// throw new AssertionError("dead");
}
}
}
long beta = sign == -1 ? PP-1 : 1;
for(int k = 0;k <= 2*r;k++){
if(betanums[k] > 0){
beta = mul(beta, betanums[k], PP);
}
}
long po = pow(fact[j*p], beta, P);
ret = mul(ret, po, P);
}
if(p == 2 && ((u*2%8 >= 3 && u*2%8 < 7) != (ret % 4 == 3)))ret = P-ret;
outer2:
for(int j = 1;j <= q-1;j++){
long cell = mul(mul(fact[j*p+v], ifact[j*p], P), ifact[v], P);
long[] alphanums = new long[q];
long sign = 1;
for(int i = 0;i <= q-1;i++){
if(i != j){
alphanums[i] = u-i;
if(u-i == 0)continue outer2;
if(alphanums[i] < 0){
sign *= -1;
alphanums[i] *= -1;
}
}
}
for(int i = 0;i <= q-1;i++){
if(i != j){
long w = j-i;
if(w < 0){
sign *= -1;
w *= -1;
}
for(int k = 0;k <= q-1;k++){
if(alphanums[k] != 0){
long g = gcd(alphanums[k], w);
alphanums[k] /= g;
w /= g;
}
}
if(w != 1){
// throw new AssertionError("dead2");
}
}
}
long alpha = sign == -1 ? PP-1 : 1;
for(int k = 0;k <= q-1;k++){
if(alphanums[k] > 0){
alpha = mul(alpha, alphanums[k], PP);
}
}
// tr("alpha", j, r, cell, alpha);
long po = pow(cell, alpha, P);
ret = mul(ret, po, P);
}
if(plused){
return ret % (P/p);
}else{
return ret;
}
}
public static long gcd(long a, long b) {
while (b > 0) {
long c = a;
a = b;
b = c % b;
}
return a;
}
public static long mul(long a, long b, long mod)
{
return a*b%mod;
// if(a >= mod || a < 0)a %= mod;
// if(a < 0)a += mod;
// if(b >= mod || b < 0)b %= mod;
// if(b < 0)b += mod;
//
// long ret = 0;
// int x = 63-Long.numberOfLeadingZeros(b);
// for(;x >= 0;x--){
// ret += ret;
// if(ret >= mod)ret -= mod;
// if(b<<~x<0){
// ret += a;
// if(ret >= mod)ret -= mod;
// }
// }
// 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 void main(String[] args) {
new G().run();
}
public void run()
{
long S = System.currentTimeMillis();
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new FastWriter(System.out);
solve();
out.flush();
long G = System.currentTimeMillis();
tr(G-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();
}
private boolean eof()
{
if(lenbuf == -1)return true;
int lptr = ptrbuf;
while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
try {
is.mark(1000);
while(true){
int b = is.read();
if(b == -1){
is.reset();
return true;
}else if(!isSpaceChar(b)){
is.reset();
return false;
}
}
} catch (IOException e) {
return true;
}
}
private final 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){
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 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[] 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 int ni()
{
int num = 0, 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 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();
}
}
public static class FastWriter
{
private static final int BUF_SIZE = 1<<13;
private final byte[] buf = new byte[BUF_SIZE];
private final OutputStream out;
private int ptr = 0;
private FastWriter(){out = null;}
public FastWriter(OutputStream os)
{
this.out = os;
}
public FastWriter(String path)
{
try {
this.out = new FileOutputStream(path);
} catch (FileNotFoundException e) {
throw new RuntimeException("FastWriter");
}
}
public FastWriter write(byte b)
{
buf[ptr++] = b;
if(ptr == BUF_SIZE)innerflush();
return this;
}
public FastWriter write(char c)
{
return write((byte)c);
}
public FastWriter write(char[] s)
{
for(char c : s){
buf[ptr++] = (byte)c;
if(ptr == BUF_SIZE)innerflush();
}
return this;
}
public FastWriter write(String s)
{
s.chars().forEach(c -> {
buf[ptr++] = (byte)c;
if(ptr == BUF_SIZE)innerflush();
});
return this;
}
private static int countDigits(int l) {
if (l >= 1000000000) return 10;
if (l >= 100000000) return 9;
if (l >= 10000000) return 8;
if (l >= 1000000) return 7;
if (l >= 100000) return 6;
if (l >= 10000) return 5;
if (l >= 1000) return 4;
if (l >= 100) return 3;
if (l >= 10) return 2;
return 1;
}
public FastWriter write(int x)
{
if(x == Integer.MIN_VALUE){
return write((long)x);
}
if(ptr + 12 >= BUF_SIZE)innerflush();
if(x < 0){
write((byte)'-');
x = -x;
}
int d = countDigits(x);
for(int i = ptr + d - 1;i >= ptr;i--){
buf[i] = (byte)('0'+x%10);
x /= 10;
}
ptr += d;
return this;
}
private static int countDigits(long l) {
if (l >= 1000000000000000000L) return 19;
if (l >= 100000000000000000L) return 18;
if (l >= 10000000000000000L) return 17;
if (l >= 1000000000000000L) return 16;
if (l >= 100000000000000L) return 15;
if (l >= 10000000000000L) return 14;
if (l >= 1000000000000L) return 13;
if (l >= 100000000000L) return 12;
if (l >= 10000000000L) return 11;
if (l >= 1000000000L) return 10;
if (l >= 100000000L) return 9;
if (l >= 10000000L) return 8;
if (l >= 1000000L) return 7;
if (l >= 100000L) return 6;
if (l >= 10000L) return 5;
if (l >= 1000L) return 4;
if (l >= 100L) return 3;
if (l >= 10L) return 2;
return 1;
}
public FastWriter write(long x)
{
if(x == Long.MIN_VALUE){
return write("" + x);
}
if(ptr + 21 >= BUF_SIZE)innerflush();
if(x < 0){
write((byte)'-');
x = -x;
}
int d = countDigits(x);
for(int i = ptr + d - 1;i >= ptr;i--){
buf[i] = (byte)('0'+x%10);
x /= 10;
}
ptr += d;
return this;
}
public FastWriter write(double x, int precision)
{
if(x < 0){
write('-');
x = -x;
}
x += Math.pow(10, -precision)/2;
// if(x < 0){ x = 0; }
write((long)x).write(".");
x -= (long)x;
for(int i = 0;i < precision;i++){
x *= 10;
write((char)('0'+(int)x));
x -= (int)x;
}
return this;
}
public FastWriter writeln(char c){ return write(c).writeln(); }
public FastWriter writeln(int x){ return write(x).writeln(); }
public FastWriter writeln(long x){ return write(x).writeln(); }
public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }
public FastWriter write(int... xs)
{
boolean first = true;
for(int x : xs) {
if (!first) write(' ');
first = false;
write(x);
}
return this;
}
public FastWriter write(long... xs)
{
boolean first = true;
for(long x : xs) {
if (!first) write(' ');
first = false;
write(x);
}
return this;
}
public FastWriter write(IntUnaryOperator f, int... xs)
{
boolean first = true;
for(int x : xs) {
if (!first) write(' ');
first = false;
write(f.applyAsInt(x));
}
return this;
}
public FastWriter write(LongUnaryOperator f, long... xs)
{
boolean first = true;
for(long x : xs) {
if (!first) write(' ');
first = false;
write(f.applyAsLong(x));
}
return this;
}
public FastWriter writeln()
{
return write((byte)'\n');
}
public FastWriter writeln(int... xs) { return write(xs).writeln(); }
public FastWriter writeln(long... xs) { return write(xs).writeln(); }
public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }
public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }
public FastWriter writeln(char[] line) { return write(line).writeln(); }
public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }
public FastWriter writeln(String s) { return write(s).writeln(); }
private void innerflush()
{
try {
out.write(buf, 0, ptr);
ptr = 0;
} catch (IOException e) {
throw new RuntimeException("innerflush");
}
}
public void flush()
{
innerflush();
try {
out.flush();
} catch (IOException e) {
throw new RuntimeException("flush");
}
}
public FastWriter print(byte b) { return write(b); }
public FastWriter print(char c) { return write(c); }
public FastWriter print(char[] s) { return write(s); }
public FastWriter print(String s) { return write(s); }
public FastWriter print(int x) { return write(x); }
public FastWriter print(long x) { return write(x); }
public FastWriter print(double x, int precision) { return write(x, precision); }
public FastWriter println(char c){ return writeln(c); }
public FastWriter println(int x){ return writeln(x); }
public FastWriter println(long x){ return writeln(x); }
public FastWriter println(double x, int precision){ return writeln(x, precision); }
public FastWriter print(int... xs) { return write(xs); }
public FastWriter print(long... xs) { return write(xs); }
public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }
public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }
public FastWriter println(int... xs) { return writeln(xs); }
public FastWriter println(long... xs) { return writeln(xs); }
public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }
public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }
public FastWriter println(char[] line) { return writeln(line); }
public FastWriter println(char[]... map) { return writeln(map); }
public FastWriter println(String s) { return writeln(s); }
public FastWriter println() { return writeln(); }
}
public static void trnz(int... o)
{
for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
System.out.println();
}
// print ids which are 1
public static void trt(long... o)
{
Queue<Integer> stands = new ArrayDeque<>();
for(int i = 0;i < o.length;i++){
for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
}
System.out.println(stands);
}
public static void tf(boolean... r)
{
for(boolean x : r)System.out.print(x?'#':'.');
System.out.println();
}
public static void tf(boolean[]... b)
{
for(boolean[] r : b) {
for(boolean x : r)System.out.print(x?'#':'.');
System.out.println();
}
System.out.println();
}
public void tf(long[]... b)
{
if(INPUT.length() != 0) {
for (long[] r : b) {
for (long x : r) {
for (int i = 0; i < 64; i++) {
System.out.print(x << ~i < 0 ? '#' : '.');
}
}
System.out.println();
}
System.out.println();
}
}
public void tf(long... b)
{
if(INPUT.length() != 0) {
for (long x : b) {
for (int i = 0; i < 64; i++) {
System.out.print(x << ~i < 0 ? '#' : '.');
}
}
System.out.println();
}
}
private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}