結果
| 問題 |
No.1691 Badugi
|
| コンテスト | |
| ユーザー |
 uwi
|
| 提出日時 | 2021-09-25 17:23:48 |
| 言語 | Java (openjdk 23) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 17,178 bytes |
| コンパイル時間 | 5,302 ms |
| コンパイル使用メモリ | 94,192 KB |
| 実行使用メモリ | 46,204 KB |
| 最終ジャッジ日時 | 2024-07-05 12:09:00 |
| 合計ジャッジ時間 | 8,676 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 * 14 RE * 3 |
ソースコード
package contest210924;
import java.io.*;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class F3 {
InputStream is;
FastWriter out;
String INPUT = "";
public static class CombinationParser
{
final int mod;
final int[][] fif;
public CombinationParser(int mod, int n){
this.mod = mod;
this.fif = enumFIF(n, mod);
}
char[] s;
int pos, len;
Map<String, Long> values;
public long parsei(String S, Map<String, Integer> values){
this.values = new HashMap<>();
for(String key : values.keySet()){
this.values.put(key, values.get(key).longValue());
}
return parse(S, this.values);
}
public long parse(String S, Map<String, Long> values){
s = S.replace(" ", "").toCharArray();
pos = 0;
len = s.length;
this.values = values;
long res = exprpm();
if(pos != len)throw new AssertionError("pos != len: " + pos + " " + len);
return res;
}
// +-
long exprpm()
{
long v = exprmd();
while(pos < len){
if(s[pos] == '+'){
pos++;
v += exprmd();
}else if(s[pos] == '-'){
pos++;
v -= exprmd();
}else{
break;
}
}
v %= mod;
if(v < 0)v += mod;
return v;
}
// */
long exprmd()
{
long v = expre();
while(pos < len){
if(s[pos] == '*'){
if(pos+1 < len && s[pos+1] == '*'){
break;
}
pos++;
v = v * expre() % mod;
}else if(s[pos] == '/'){
pos++;
long res = expre();
if(res == 0)throw new AssertionError("divide by zero: " + pos);
v = v * invl(res, mod) % mod;
}else if(s[pos] == '+' || s[pos] == '-' || s[pos] == ')' || s[pos] == ',') {
break;
}else{
// 乗算とみなす
v = v * expre() % mod;
break;
}
}
v %= mod;
if(v < 0)v += mod;
return v;
}
long expre()
{
long v = expr();
if(pos >= len)return v;
if(s[pos] == '*' && pos+1 < len && s[pos+1] == '*'){
pos+=2;
v = pow(v, expr(), mod);
}else if(s[pos] == '^') {
pos++;
v = pow(v, expr(), mod);
}
return v;
}
long expr()
{
if(s[pos] == '('){
pos++;
long res = exprpm();
expect(')');
pos++;
if(pos < len && s[pos] == '!'){
res = fif[0][(int)res];
pos++;
}
return res;
}else if(s[pos] == '-'){
// 単項minus
pos++;
long res = item();
res = -res;
if(res < 0)res += mod;
return res;
}else{
return item();
}
}
void expect(char c)
{
if(s[pos] != c)throw new AssertionError("expect '" + c + "' @" + pos);
}
long item()
{
if(s[pos] == 'C' && pos+1 < len && s[pos+1] == '('){
pos++;
pos++;
long n = exprpm(); // FIXME: modではない
expect(',');
pos++;
long r = exprpm();
expect(')');
pos++;
return C((int)n, (int)r, mod, fif);
}else if('0' <= s[pos] && s[pos] <= '9'){
// 即値
long val = 0;
while(pos < len && '0' <= s[pos] && s[pos] <= '9'){
val = (val * 10 + s[pos]-'0') % mod;
pos++;
}
long res = val;
if(pos < len && s[pos] == '!'){
res = fif[0][(int)res];
pos++;
}
return res;
}else{
// 変数
StringBuilder v = new StringBuilder();
while(pos < len && (
'a' <= s[pos] && s[pos] <= 'z' ||
'A' <= s[pos] && s[pos] <= 'Z' ||
'0' <= s[pos] && s[pos] <= '9'
)){
v.append(s[pos]);
pos++;
}
if (!values.containsKey(v.toString())) {
throw new AssertionError("undefined variable: " + v + " @" + pos);
}
long res = values.get(v.toString());
if(pos < len && s[pos] == '!'){
res = fif[0][(int)res];
pos++;
}
return res;
}
}
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 C(int n, int r, int mod, int[][] fif) {
if (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};
}
}
public static final int mod = 998244353;
public void solve()
{
int n = ni(), m = ni(), K = ni();
var ps = new CombinationParser(998244353, 1000005);
var params = Map.of("n", n, "m", m, "k", K);
long D = ps.parsei("C(n,k-2)*C(m,k-2)*(k-2)!", params);
long r1 = ps.parsei("C(n,k-1)*C(m,k-1)*(k-4)!*C(k-1,3)**2*9", params);
long o2n = ps.parsei("C(k-2,2)*C(m-(k-2),2)*2/4 + C(k-2,2)*C(n-(k-2),2)*2/4", params);
long o2v = ps.parsei("C(k-2,2)*(m-(k-2)) + C(k-2,2)*(n-(k-2))", params);
long o2h = ps.parsei("(C(n,k-3)*C(m,k-3)*(k-3)!*C(m-(k-3),3)*(n-(k-3)) + C(n,k-3)*C(m,k-3)*(k-3)!*C(n-(k-3),3)*(m-(k-3)))", params);
long o1n = ps.parsei("(((k-2)**2-(k-2))*(k-2-2)*(m-(k-2)) + ((k-2)**2-(k-2))*(k-2-2)*(n-(k-2)))/2", params);
long o1h = ps.parsei("(((k-2)**2-(k-2))*(m-(k-2)) + ((k-2)**2-(k-2))*(n-(k-2)))/2", params);
long o0n = ps.parsei("1/2*C(k-2,2)", params);
long o0h = ps.parsei("2*(k-2)*C(k-3,2)", params);
long o0l = ps.parsei("C(k-2,3)*3*2", params);
long o0i = ps.parsei("C(k-2,2)*C(k-4,2)/2*4", params);
long ans = r1 + o2n * D + o2v * D + o2h + o1n * D + o1h * D + o0n * D + o0h * D + o0l * D + o0i * D;
out.println(ans%mod);
}
public static void main(String[] args) {
new F3().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[] 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)); }
}