結果
| 問題 | No.2181 LRM Question 2 |
| ユーザー |
 uwi
|
| 提出日時 | 2023-01-07 01:22:29 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 1,405 ms / 2,000 ms |
| コード長 | 18,590 bytes |
| コンパイル時間 | 6,009 ms |
| コンパイル使用メモリ | 93,624 KB |
| 実行使用メモリ | 45,828 KB |
| 最終ジャッジ日時 | 2024-05-08 01:00:46 |
| 合計ジャッジ時間 | 13,545 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 74 ms
37,664 KB |
| testcase_01 | AC | 69 ms
37,928 KB |
| testcase_02 | AC | 767 ms
43,164 KB |
| testcase_03 | AC | 63 ms
37,840 KB |
| testcase_04 | AC | 65 ms
37,700 KB |
| testcase_05 | AC | 68 ms
37,888 KB |
| testcase_06 | AC | 67 ms
37,992 KB |
| testcase_07 | AC | 68 ms
37,804 KB |
| testcase_08 | AC | 987 ms
43,216 KB |
| testcase_09 | AC | 361 ms
43,512 KB |
| testcase_10 | AC | 1,288 ms
43,168 KB |
| testcase_11 | AC | 1,405 ms
43,448 KB |
| testcase_12 | AC | 1,387 ms
43,164 KB |
| testcase_13 | AC | 74 ms
37,968 KB |
| testcase_14 | AC | 104 ms
45,528 KB |
| testcase_15 | AC | 73 ms
38,088 KB |
| testcase_16 | AC | 130 ms
45,828 KB |
| testcase_17 | AC | 114 ms
39,136 KB |
| testcase_18 | AC | 92 ms
38,956 KB |
| testcase_19 | AC | 78 ms
38,244 KB |
| testcase_20 | AC | 90 ms
39,992 KB |
| testcase_21 | AC | 210 ms
40,740 KB |
| testcase_22 | AC | 91 ms
39,292 KB |
| testcase_23 | AC | 64 ms
37,840 KB |
| testcase_24 | AC | 64 ms
37,608 KB |
| testcase_25 | AC | 61 ms
37,704 KB |
ソースコード
package contest230106;
import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class G5 {
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
CombinationGeneralMultipleSmall cgm = new CombinationGeneralMultipleSmall(mod);
long ans = -2*(R-L+1);
long s = 0;
for(int i = 0;i < R-L+1;i++){
long n = L+i;
// long val = cgm.C(2*n, n);
long val = cgm.Center(n);
s += val;
}
ans += s;
ans %= mod;
if(ans < 0)ans += mod;
out.println(ans);
}
public static class CombinationGeneralMultipleSmall {
int[][] f;
long[][] pesmap;
int[] qmap;
long[][] aprs;
public CombinationGeneralMultipleSmall(int mod)
{
int[] primes = sieveEratosthenes((int)Math.sqrt(mod));
f = factor(mod, primes);
pesmap = new long[f.length][];
qmap = new int[f.length];
for(int j = 0;j < f.length;j++){
int[] u = f[j];
int P = u[0], e = u[1];
int Q = (int)Math.pow(P, e);
long[] pes = new long[Q];
pes[0] = 1;
for(int i = 1;i < Q;i++){
if(i % P == 0){
pes[i] = pes[i-1];
}else{
pes[i] = pes[i-1] * i % Q;
}
}
pesmap[j] = pes;
qmap[j] = Q;
}
aprs = aprs(qmap);
}
public long C(long n, long m)
{
if(m < 0 || m > n)return 0L;
long[] mods = new long[f.length];
for(int i = 0;i < f.length;i++){
mods[i] = C(n, m, i);
}
return crt(qmap, mods, aprs);
}
private long C(long n, long m, int pind)
{
if(m < 0 || m > n)return 0L;
int P = f[pind][0], e = f[pind][1];
long pe = 0;
int mod = qmap[pind];
long num = 1;
long den = 1;
for(long x = n;x > 0;x /= P){
num = num * F(x, pind) % mod;
pe += x/P;
}
for(long x = m;x > 0;x /= P){
den = den * F(x, pind) % mod;
pe -= x/P;
}
for(long x = n-m;x > 0;x /= P){
den = den * F(x, pind) % mod;
pe -= x/P;
}
if(pe >= e)return 0L;
num = num * invl(den, mod) % mod;
for(int i = 0;i < pe;i++){
num = num * P % mod;
}
// System.err.println(Arrays.toString(new long[]{n, m, P, e, num}));
return num;
}
public long Center(long n)
{
long[] mods = new long[f.length];
for(int i = 0;i < f.length;i++){
mods[i] = Center(n, i);
}
return crt(qmap, mods, aprs);
}
private long Center(long n, int pind)
{
int P = f[pind][0], e = f[pind][1];
long pe = 0;
int mod = qmap[pind];
long num = 1;
long den = 1;
for(long x = 2*n;x > 0;x /= P){
num = num * F(x, pind) % mod;
pe += x/P;
}
long minus = 0;
for(long x = n;x > 0;x /= P){
den = den * F(x, pind) % mod;
minus += x/P;
}
pe -= 2*minus;
den = den * den % mod;
if(pe >= e)return 0L;
num = num * invl(den, mod) % mod;
for(int i = 0;i < pe;i++){
num = num * P % mod;
}
return num;
}
public static long[][] aprs(int[] divs)
{
if(divs.length == 0)return null;
long div = divs[0];
long[][] ret = new long[divs.length][];
for(int i = 1;i < divs.length;i++){
ret[i] = exgcd(div, divs[i]);
div = div * divs[i];
}
return ret;
}
public static long crt(final int[] divs, final long[] mods, long[][] aprs)
{
if(divs.length == 0)return 0L;
long div = divs[0];
long mod = mods[0];
for(int i = 1;i < divs.length;i++){
long[] apr = aprs[i];
long ndiv = div * divs[i];
mod += ((mods[i]-mod)*apr[1]%divs[i]) * div;
div = ndiv;
}
mod %= div;
if(mod < 0)mod += div;
return mod;
}
public static long[] exgcd(long a, long b)
{
if(a == 0 || b == 0)return null;
int as = Long.signum(a);
int bs = Long.signum(b);
a = Math.abs(a); b = Math.abs(b);
long p = 1, q = 0, r = 0, s = 1;
while(b > 0){
long c = a / b;
long d;
d = a; a = b; b = d % b;
d = p; p = q; q = d - c * q;
d = r; r = s; s = d - c * s;
}
return new long[]{a, p * as, r * bs};
}
public long FNaive(int n, int P, int e)
{
long mod = 1;
for(int i = 0;i < e;i++)mod = mod * P;
long ret = 1;
for(int i = 1;i <= n;i++){
if(i % P == 0)continue;
ret = ret * i % mod;
}
return ret;
}
public long F(long n, int pind)
{
int mod = qmap[pind];
long[] pes = pesmap[pind];
assert pes[mod-1] == 1 || pes[mod-1] == mod-1;
long ret = pes[(int)(n%mod)];
if(pes[mod-1] == mod-1 && n/mod%2 == 1){
ret = mod-ret;
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 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 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 void main(String[] args) {
new G5().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)); }
}