結果
| 問題 | No.2313 Product of Subsequence (hard) |
| ユーザー |
 遭難者
|
| 提出日時 | 2023-05-24 10:41:15 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 25,235 bytes |
| コンパイル時間 | 3,622 ms |
| コンパイル使用メモリ | 87,168 KB |
| 実行使用メモリ | 69,848 KB |
| 最終ジャッジ日時 | 2023-08-25 13:04:11 |
| 合計ジャッジ時間 | 10,925 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge12 |
（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 | 38 ms
51,352 KB |
| testcase_01 | AC | 37 ms
49,704 KB |
| testcase_02 | AC | 41 ms
51,340 KB |
| testcase_03 | AC | 47 ms
51,116 KB |
| testcase_04 | AC | 51 ms
52,280 KB |
| testcase_05 | AC | 61 ms
53,584 KB |
| testcase_06 | AC | 45 ms
51,404 KB |
| testcase_07 | AC | 52 ms
52,380 KB |
| testcase_08 | AC | 461 ms
61,616 KB |
| testcase_09 | AC | 163 ms
57,340 KB |
| testcase_10 | AC | 312 ms
65,232 KB |
| testcase_11 | AC | 165 ms
57,556 KB |
| testcase_12 | AC | 286 ms
65,516 KB |
| testcase_13 | TLE | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
ソースコード
import java.util.*;
import java.io.*;
class Main {
private static final long solve(int n, int k, long[] input) {
if (k == 1) {
long ans = mp(2, n) - 1;
if ((ans %= mod) < 0)
ans += mod;
return ans;
}
var tt = p(k);
int m = tt.size();
var t = new long[m];
int ttt = 0;
for (long i : tt)
t[ttt++] = i;
Arrays.sort(t);
var c = new int[m];
for (int i = 0; i < n; i++)
c[Arrays.binarySearch(t, g(input[i], k))]++;
var d = new long[m];
d[0] = 1L;
fa = new long[n + 1];
fai = new long[n + 1];
fa[0] = 1L;
for (int i = 1; i <= n; i++)
fa[i] = i * fa[i - 1] % mod;
fai[n] = mp(fa[n], mod - 2);
for (int i = n; i > 0; i--)
fai[i - 1] = i * fai[i] % mod;
for (int x = 1; x < m; x++) {
final int len = c[x];
var dd = new long[m];
var cc1 = new long[len + 1];
var cc2 = new long[len + 1];
for (int i = 0; i <= len; i++)
cc1[i] = cc2[i] = comb(len, i);
for (int i = len; i > 0; i--)
if ((cc2[i - 1] += cc2[i]) >= mod)
cc2[i - 1] -= mod;
for (int i = 0; i < m; i++) {
int loop = 0;
long now = t[i];
long before_now = -1;
while (true) {
if (before_now == now || loop > len)
break;
int key = Arrays.binarySearch(t, now);
if (key < 0)
break;
dd[key] += d[i] * cc1[loop];
dd[key] %= mod;
now = g(now * t[x], k);
loop++;
}
if (loop <= len) {
int key = Arrays.binarySearch(t, now);
dd[key] += d[i] * cc2[loop];
dd[key] %= mod;
}
}
d = dd;
}
// ou.println(d[m - 1]);
return d[m - 1] * mp(2, c[0]) % mod;
}
private static final void start() throws IOException {
boolean submit = true;
if (submit) {
int t = 1;
// t = ni();
for (int i = 0; i < t; i++) {
int n = ni(), k = ni();
long[] a = nl(n);
long ans = solve(n, k, a);
ou.println(ans);
}
} else {
var rand = new Random();
for (int jud = 1; jud <= 10000; jud++) {
int n = rand.nextInt(10) + 3;
int k = rand.nextInt(20) + 2;
var a = new long[n];
for (int i = 0; i < n; i++)
a[i] = rand.nextInt(20) + 1;
long ans1 = solve(n, k, a);
long ans2 = gu(n, k, a);
if (ans1 != ans2) {
ou.println(ans1 + " " + ans2);
ou.println(n + " " + k);
ou.print(a);
break;
}
}
}
}
private static final int mod = 998244353;
private static long[] fa, fai;
private static final long comb(int n, int k) {
return fai[k] * fai[n - k] % mod * fa[n] % mod;
}
private static final long gu(int n, long k, long[] input) {
var a = new long[n];
for (int i = 0; i < n; i++)
a[i] = input[i] % k;
long ans = 0;
int nn = 1 << n;
for (int i = 1; i < nn; i++) {
long mul = 1L;
for (int j = 0; j < n; j++) {
if (((i >> j) & 1) == 1)
mul = mul * a[j] % k;
}
if (mul == 0)
ans++;
}
return ans;
}
private static final long mp(long a, int b) {
if (b == 0)
return 1L;
if ((b & 1) == 0)
return mp(a * a % mod, b >> 1);
return mp(a, b - 1) * a % mod;
}
private static final ArrayList<Long> p(long n) {
var t = new ArrayList<Long>();
long i = 1;
while (i * i < n) {
if (n % i == 0) {
t.add(i);
t.add(n / i);
}
i++;
}
if (i * i == n)
t.add(i);
return t;
}
private static final long g(long x, long y) {
return y == 0 ? x : g(y, x % y);
}
public static void main(String[] args) throws IOException {
start();
ou.flush();
}
private static final int ni() throws IOException {
return sc.nextInt();
}
private static final int[] ni(int n) throws IOException {
return sc.nextIntArray(n);
}
private static final long nl() throws IOException {
return sc.nextLong();
}
private static final long[] nl(int n) throws IOException {
return sc.nextLongArray(n);
}
private static final String ns() throws IOException {
return sc.next();
}
private static final char[] nc() throws IOException {
return sc.nextCharArray();
}
private static final double nd() throws IOException {
return sc.nextDouble();
}
private static final ContestInputStream sc = new ContestInputStream();
private static final ContestOutputStream ou = new ContestOutputStream();
}
final class ContestInputStream extends FilterInputStream {
protected final byte[] buf;
protected int pos = 0;
protected int lim = 0;
private final char[] cbuf;
public ContestInputStream() {
super(System.in);
this.buf = new byte[1 << 13];
this.cbuf = new char[1 << 20];
}
boolean hasRemaining() throws IOException {
if (pos < lim)
return true;
lim = in.read(buf);
pos = 0;
return lim > 0;
}
final int remaining() throws IOException {
if (pos >= lim) {
lim = in.read(buf);
pos = 0;
}
return lim - pos;
}
@Override
public final int available() throws IOException {
if (pos < lim)
return lim - pos + in.available();
return in.available();
}
@Override
public final long skip(long n) throws IOException {
if (pos < lim) {
int rem = lim - pos;
if (n < rem) {
pos += n;
return n;
}
pos = lim;
return rem;
}
return in.skip(n);
}
@Override
public final int read() throws IOException {
if (hasRemaining())
return buf[pos++];
return -1;
}
@Override
public final int read(byte[] b, int off, int len) throws IOException {
if (pos < lim) {
int rem = Math.min(lim - pos, len);
for (int i = 0; i < rem; i++)
b[off + i] = buf[pos + i];
pos += rem;
return rem;
}
return in.read(b, off, len);
}
public final char[] readToken() throws IOException {
int cpos = 0;
int rem;
byte b;
l: while ((rem = remaining()) > 0) {
for (int i = 0; i < rem; i++) {
b = buf[pos + i];
if (b <= 0x20) {
pos += i + 1;
cpos += i;
if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a)
pos++;
break l;
}
cbuf[cpos + i] = (char) b;
}
pos += rem;
cpos += rem;
}
char[] arr = new char[cpos];
for (int i = 0; i < cpos; i++)
arr[i] = cbuf[i];
return arr;
}
public final int readToken(char[] cbuf, int off) throws IOException {
int cpos = off;
int rem;
byte b;
l: while ((rem = remaining()) > 0) {
for (int i = 0; i < rem; i++) {
b = buf[pos + i];
if (b <= 0x20) {
pos += i + 1;
cpos += i;
if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a)
pos++;
break l;
}
cbuf[cpos + i] = (char) b;
}
pos += rem;
cpos += rem;
}
return cpos - off;
}
public final int readToken(char[] cbuf) throws IOException {
return readToken(cbuf, 0);
}
public final String next() throws IOException {
int cpos = 0;
int rem;
byte b;
l: while ((rem = remaining()) > 0) {
for (int i = 0; i < rem; i++) {
b = buf[pos + i];
if (b <= 0x20) {
pos += i + 1;
cpos += i;
if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a)
pos++;
break l;
}
cbuf[cpos + i] = (char) b;
}
pos += rem;
cpos += rem;
}
return String.valueOf(cbuf, 0, cpos);
}
public final char[] nextCharArray() throws IOException {
return readToken();
}
public final int nextInt() throws IOException {
if (!hasRemaining())
return 0;
int value = 0;
byte b = buf[pos++];
if (b == 0x2d) {
while (hasRemaining() && (b = buf[pos++]) > 0x20)
value = (value << 3) + (value << 1) - b + 0x30;
} else {
do {
value = (value << 3) + (value << 1) + b - 0x30;
} while (hasRemaining() && (b = buf[pos++]) > 0x20);
}
if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a)
pos++;
return value;
}
public final long nextLong() throws IOException {
if (!hasRemaining())
return 0L;
long value = 0L;
byte b = buf[pos++];
if (b == 0x2d) {
while (hasRemaining() && (b = buf[pos++]) > 0x20)
value = (value << 3) + (value << 1) - b + 0x30;
} else {
do {
value = (value << 3) + (value << 1) + b - 0x30;
} while (hasRemaining() && (b = buf[pos++]) > 0x20);
}
if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a)
pos++;
return value;
}
public final char nextChar() throws IOException {
if (!hasRemaining())
throw new EOFException();
final char c = (char) buf[pos++];
if (hasRemaining() && buf[pos++] == 0x0d && hasRemaining() && buf[pos] == 0x0a)
pos++;
return c;
}
public final float nextFloat() throws IOException {
return Float.parseFloat(next());
}
public final double nextDouble() throws IOException {
return Double.parseDouble(next());
}
public final boolean[] nextBooleanArray(char ok) throws IOException {
char[] s = readToken();
int n = s.length;
boolean[] t = new boolean[n];
for (int i = 0; i < n; i++)
t[i] = s[i] == ok;
return t;
}
public final boolean[][] nextBooleanMatrix(int h, int w, char ok) throws IOException {
boolean[][] s = new boolean[h][];
for (int i = 0; i < h; i++) {
char[] t = readToken();
int n = t.length;
s[i] = new boolean[n];
for (int j = 0; j < n; j++)
s[i][j] = t[j] == ok;
}
return s;
}
public final String[] nextStringArray(int len) throws IOException {
String[] arr = new String[len];
for (int i = 0; i < len; i++)
arr[i] = next();
return arr;
}
public final int[] nextIntArray(int len) throws IOException {
int[] arr = new int[len];
for (int i = 0; i < len; i++)
arr[i] = nextInt();
return arr;
}
public final int[] nextIntArray(int len, java.util.function.IntUnaryOperator map) throws IOException {
int[] arr = new int[len];
for (int i = 0; i < len; i++)
arr[i] = map.applyAsInt(nextInt());
return arr;
}
public final long[] nextLongArray(int len, java.util.function.LongUnaryOperator map) throws IOException {
long[] arr = new long[len];
for (int i = 0; i < len; i++)
arr[i] = map.applyAsLong(nextLong());
return arr;
}
public final int[][] nextIntMatrix(int h, int w) throws IOException {
int[][] arr = new int[h][w];
for (int i = 0; i < h; i++)
for (int j = 0; j < w; j++)
arr[i][j] = nextInt();
return arr;
}
public final int[][] nextIntMatrix(int h, int w, java.util.function.IntUnaryOperator map) throws IOException {
int[][] arr = new int[h][w];
for (int i = 0; i < h; i++)
for (int j = 0; j < w; j++)
arr[i][j] = map.applyAsInt(nextInt());
return arr;
}
public final long[] nextLongArray(int len) throws IOException {
long[] arr = new long[len];
for (int i = 0; i < len; i++)
arr[i] = nextLong();
return arr;
}
public final long[][] nextLongMatrix(int h, int w) throws IOException {
long[][] arr = new long[h][w];
for (int i = 0; i < h; i++)
for (int j = 0; j < w; j++)
arr[i][j] = nextLong();
return arr;
}
public final float[] nextFloatArray(int len) throws IOException {
float[] arr = new float[len];
for (int i = 0; i < len; i++)
arr[i] = nextFloat();
return arr;
}
public final double[] nextDoubleArray(int len) throws IOException {
double[] arr = new double[len];
for (int i = 0; i < len; i++)
arr[i] = nextDouble();
return arr;
}
public final char[][] nextCharMatrix(int h, int w) throws IOException {
char[][] arr = new char[h][];
for (int i = 0; i < h; i++)
arr[i] = readToken();
return arr;
}
public final void nextThrow() throws IOException {
next();
return;
}
public final void nextThrow(int n) throws IOException {
for (int i = 0; i < n; i++)
nextThrow();
return;
}
}
final class ContestOutputStream extends FilterOutputStream implements Appendable {
protected final byte[] buf;
protected int pos = 0;
public ContestOutputStream() {
super(System.out);
this.buf = new byte[1 << 13];
}
@Override
public void flush() throws IOException {
out.write(buf, 0, pos);
pos = 0;
out.flush();
}
void put(byte b) throws IOException {
if (pos >= buf.length)
flush();
buf[pos++] = b;
}
int remaining() throws IOException {
if (pos >= buf.length)
flush();
return buf.length - pos;
}
@Override
public void write(int b) throws IOException {
put((byte) b);
}
@Override
public void write(byte[] b, int off, int len) throws IOException {
int o = off;
int l = len;
while (l > 0) {
int rem = Math.min(remaining(), l);
for (int i = 0; i < rem; i++)
buf[pos + i] = b[o + i];
pos += rem;
o += rem;
l -= rem;
}
}
@Override
public ContestOutputStream append(char c) throws IOException {
put((byte) c);
return this;
}
@Override
public ContestOutputStream append(CharSequence csq, int start, int end) throws IOException {
int off = start;
int len = end - start;
while (len > 0) {
int rem = Math.min(remaining(), len);
for (int i = 0; i < rem; i++)
buf[pos + i] = (byte) csq.charAt(off + i);
pos += rem;
off += rem;
len -= rem;
}
return this;
}
@Override
public ContestOutputStream append(CharSequence csq) throws IOException {
return append(csq, 0, csq.length());
}
public ContestOutputStream append(char[] arr, int off, int len) throws IOException {
int o = off;
int l = len;
while (l > 0) {
int rem = Math.min(remaining(), l);
for (int i = 0; i < rem; i++)
buf[pos + i] = (byte) arr[o + i];
pos += rem;
o += rem;
l -= rem;
}
return this;
}
public ContestOutputStream print(char[] arr) throws IOException {
return append(arr, 0, arr.length).newLine();
}
public ContestOutputStream print(boolean value) throws IOException {
if (value)
return append("o");
return append(".");
}
public ContestOutputStream println(boolean value) throws IOException {
if (value)
return append("o\n");
return append(".\n");
}
public ContestOutputStream print(boolean[][] value) throws IOException {
final int n = value.length, m = value[0].length;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++)
print(value[i][j]);
newLine();
}
return this;
}
public ContestOutputStream print(int value) throws IOException {
return append(String.valueOf(value));
}
public ContestOutputStream println(int value) throws IOException {
return append(String.valueOf(value)).newLine();
}
public ContestOutputStream print(long value) throws IOException {
return append(String.valueOf(value));
}
public ContestOutputStream println(long value) throws IOException {
return append(String.valueOf(value)).newLine();
}
public ContestOutputStream print(float value) throws IOException {
return append(String.valueOf(value));
}
public ContestOutputStream println(float value) throws IOException {
return append(String.valueOf(value)).newLine();
}
private ContestOutputStream dtos(double x, int n) throws IOException {
if (x < 0) {
append('-');
x = -x;
}
x += Math.pow(10, -n) / 2;
long longx = (long) x;
print(longx);
append('.');
x -= longx;
for (int i = 0; i < n; i++) {
x *= 10;
int intx = (int) x;
print(intx);
x -= intx;
}
return this;
}
public ContestOutputStream print(double value) throws IOException {
return dtos(value, 20);
}
public ContestOutputStream println(double value) throws IOException {
return dtos(value, 20).newLine();
}
public ContestOutputStream print(char value) throws IOException {
return append(value);
}
public ContestOutputStream println(char value) throws IOException {
return append(value).newLine();
}
public ContestOutputStream print(String value) throws IOException {
return append(value);
}
public ContestOutputStream println(String value) throws IOException {
return append(String.valueOf(value)).newLine();
}
public ContestOutputStream print(Object value) throws IOException {
return append(String.valueOf(value));
}
public ContestOutputStream println(Object value) throws IOException {
return append(String.valueOf(value)).newLine();
}
public ContestOutputStream printYN(boolean yes) throws IOException {
if (yes)
return println("Yes");
return println("No");
}
public ContestOutputStream printAB(boolean yes) throws IOException {
if (yes)
return println("Alice");
return println("Bob");
}
public ContestOutputStream print(CharSequence[] arr) throws IOException {
if (arr.length > 0) {
append(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').append(arr[i]);
}
return this;
}
public ContestOutputStream print(int[] arr) throws IOException {
if (arr.length > 0) {
print(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').print(arr[i]);
}
newLine();
return this;
}
public ContestOutputStream print(int[] arr, int length) throws IOException {
if (length > 0)
print(arr[0]);
for (int i = 1; i < length; i++)
append('\u0020').print(arr[i]);
newLine();
return this;
}
public ContestOutputStream println(int[] arr) throws IOException {
for (int i : arr)
print(i).newLine();
return this;
}
public ContestOutputStream println(int[] arr, int length) throws IOException {
for (int i = 0; i < length; i++)
println(arr[i]);
return this;
}
public ContestOutputStream print(boolean[] arr) throws IOException {
if (arr.length > 0) {
print(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').print(arr[i]);
}
newLine();
return this;
}
public ContestOutputStream print(long[] arr) throws IOException {
if (arr.length > 0) {
print(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').print(arr[i]);
}
newLine();
return this;
}
public ContestOutputStream print(long[] arr, int length) throws IOException {
if (length > 0)
print(arr[0]);
for (int i = 1; i < length; i++)
append('\u0020').print(arr[i]);
newLine();
return this;
}
public ContestOutputStream println(long[] arr, int length) throws IOException {
for (int i = 0; i < length; i++)
println(arr[i]);
return this;
}
public ContestOutputStream println(long[] arr) throws IOException {
for (long i : arr)
print(i).newLine();
return this;
}
public ContestOutputStream print(float[] arr) throws IOException {
if (arr.length > 0) {
print(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').print(arr[i]);
}
return this;
}
public ContestOutputStream println(float[] arr) throws IOException {
for (float i : arr)
print(i).newLine();
return this;
}
public ContestOutputStream print(double[] arr) throws IOException {
if (arr.length > 0) {
print(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').print(arr[i]);
}
return newLine();
}
public ContestOutputStream println(double[] arr) throws IOException {
for (double i : arr)
print(i).newLine();
return this;
}
public ContestOutputStream print(Object[] arr) throws IOException {
if (arr.length > 0) {
print(arr[0]);
for (int i = 1; i < arr.length; i++)
append('\u0020').print(arr[i]);
}
return newLine();
}
public ContestOutputStream print(java.util.ArrayList<?> arr) throws IOException {
if (!arr.isEmpty()) {
final int n = arr.size();
print(arr.get(0));
for (int i = 1; i < n; i++)
print(" ").print(arr.get(i));
}
return newLine();
}
public ContestOutputStream println(java.util.ArrayList<?> arr) throws IOException {
final int n = arr.size();
for (int i = 0; i < n; i++)
println(arr.get(i));
return this;
}
public ContestOutputStream newLine() throws IOException {
return append(System.lineSeparator());
}
public ContestOutputStream endl() throws IOException {
newLine().flush();
return this;
}
public ContestOutputStream print(int[][] arr) throws IOException {
for (int[] i : arr)
print(i);
return this;
}
public ContestOutputStream print(long[][] arr) throws IOException {
for (long[] i : arr)
print(i);
return this;
}
public ContestOutputStream print(char[][] arr) throws IOException {
for (char[] i : arr)
print(i);
return this;
}
public ContestOutputStream print(Object[][] arr) throws IOException {
for (Object[] i : arr)
print(i);
return this;
}
public ContestOutputStream println() throws IOException {
return newLine();
}
public ContestOutputStream println(Object... arr) throws IOException {
for (Object i : arr)
print(i);
return newLine();
}
public ContestOutputStream printToChar(int c) throws IOException {
return print((char) c);
}
}