結果

問題 No.1299 Random Array Score
ユーザー suisensuisen
提出日時 2020-11-27 21:31:12
言語 Java21
(openjdk 21)
結果
RE  
(最新)
AC  
(最初)
実行時間 -
コード長 25,307 bytes
コンパイル時間 3,218 ms
コンパイル使用メモリ 91,008 KB
実行使用メモリ 51,668 KB
最終ジャッジ日時 2023-10-01 04:51:50
合計ジャッジ時間 6,757 ms
ジャッジサーバーID
(参考情報)
judge15 / judge14
このコードへのチャレンジ
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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 RE -
testcase_01 RE -
testcase_02 RE -
testcase_03 RE -
testcase_04 RE -
testcase_05 RE -
testcase_06 RE -
testcase_07 RE -
testcase_08 RE -
testcase_09 RE -
testcase_10 RE -
testcase_11 RE -
testcase_12 RE -
testcase_13 RE -
testcase_14 RE -
testcase_15 RE -
testcase_16 RE -
testcase_17 RE -
testcase_18 RE -
testcase_19 RE -
testcase_20 RE -
testcase_21 RE -
testcase_22 RE -
testcase_23 RE -
testcase_24 RE -
testcase_25 RE -
testcase_26 RE -
testcase_27 RE -
testcase_28 RE -
testcase_29 RE -
testcase_30 RE -
testcase_31 RE -
testcase_32 RE -
testcase_33 RE -
testcase_34 RE -
testcase_35 RE -
testcase_36 RE -
権限があれば一括ダウンロードができます

ソースコード

diff #

import java.io.InputStream;
import java.util.Arrays;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class Main {
    public static void main(String[] args) throws Exception {
        ExtendedScanner sc = new ExtendedScanner();
        FastPrintStream pw = new FastPrintStream();
        solve(sc, pw);
        sc.close();
        pw.flush();
        pw.close();
    }

    static final long MOD = Const.MOD998244353;
    static final ModArithmetic MA = ModArithmetic998244353.INSTANCE;

    public static void solve(ExtendedScanner sc, FastPrintStream pw) {
        int n = sc.nextInt();
        long k = sc.nextLong();
        long[] a = sc.longs(n);
        long s = 0;
        for (long e : a) {
            s += e;
        }
        s = MA.mod(s);
        long ans = MA.mul(s, MA.pow(2, k));
        pw.println(ans);
    }
}

/**
 * @author https://atcoder.jp/users/suisen
 */
class FastScanner implements AutoCloseable {
    private final ByteBuffer tokenBuf = new ByteBuffer();
    private final java.io.InputStream in;
    private final byte[] rawBuf = new byte[1 << 14];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner(java.io.InputStream in) {
        this.in = in;
    }

    public FastScanner() {
        this(new java.io.FileInputStream(java.io.FileDescriptor.in));
    }

    private final int readByte() {
        if (ptr < buflen) return rawBuf[ptr++];
        ptr = 0;
        try {
            buflen = in.read(rawBuf);
            if (buflen > 0) {
                return rawBuf[ptr++];
            } else {
                throw new java.io.EOFException();
            }
        } catch (java.io.IOException e) {
            throw new java.io.UncheckedIOException(e);
        }
    }

    private final int readByteUnsafe() {
        if (ptr < buflen) return rawBuf[ptr++];
        ptr = 0;
        try {
            buflen = in.read(rawBuf);
            if (buflen > 0) {
                return rawBuf[ptr++];
            } else {
                return -1;
            }
        } catch (java.io.IOException e) {
            throw new java.io.UncheckedIOException(e);
        }
    }

    private final int skipUnprintableChars() {
        int b = readByte();
        while (b <= 32 || b >= 127) b = readByte();
        return b;
    }

    private final void loadToken() {
        tokenBuf.clear();
        for (int b = skipUnprintableChars(); 32 < b && b < 127; b = readByteUnsafe()) {
            tokenBuf.append(b);
        }
    }

    public final boolean hasNext() {
        for (int b = readByteUnsafe(); b <= 32 || b >= 127; b = readByteUnsafe()) {
            if (b == -1) return false;
        }
        --ptr;
        return true;
    }

    public final String next() {
        loadToken();
        return new String(tokenBuf.getRawBuf(), 0, tokenBuf.size());
    }

    public final String nextLine() {
        tokenBuf.clear();
        for (int b = readByte(); b != '\n'; b = readByteUnsafe()) {
            if (b == -1) break;
            tokenBuf.append(b);
        }
        return new String(tokenBuf.getRawBuf(), 0, tokenBuf.size());
    }

    public final char nextChar() {
        return (char) skipUnprintableChars();
    }

    public final char[] nextChars() {
        loadToken();
        return tokenBuf.toCharArray();
    }

    public final long nextLong() {
        long n = 0;
        boolean isNegative = false;
        int b = skipUnprintableChars();
        if (b == '-') {
            isNegative = true;
            b = readByteUnsafe();
        }
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while ('0' <= b && b <= '9') {
            // -9223372036854775808 - 9223372036854775807
            if (n >= 922337203685477580l) {
                if (n > 922337203685477580l) {
                    throw new ArithmeticException("long overflow");
                }
                if (isNegative) {
                    if (b >= '9') {
                        throw new ArithmeticException("long overflow");
                    }
                    n = -n - (b + '0');
                    b = readByteUnsafe();
                    if ('0' <= b && b <= '9') {
                        throw new ArithmeticException("long overflow");
                    } else if (b <= 32 || b >= 127) {
                        return n;
                    } else {
                        throw new NumberFormatException();
                    }
                } else {
                    if (b >= '8') {
                        throw new ArithmeticException("long overflow");
                    }
                    n = n * 10 + b - '0';
                    b = readByteUnsafe();
                    if ('0' <= b && b <= '9') {
                        throw new ArithmeticException("long overflow");
                    } else if (b <= 32 || b >= 127) {
                        return n;
                    } else {
                        throw new NumberFormatException();
                    }
                }
            }
            n = n * 10 + b - '0';
            b = readByteUnsafe();
        }
        if (b <= 32 || b >= 127) return isNegative ? -n : n;
        throw new NumberFormatException();
    }
    public final int nextInt() {
        long value = nextLong();
        if ((int) value != value) {
            throw new ArithmeticException("int overflow");
        }
        return (int) value;
    }
    public final double nextDouble() {
        return Double.parseDouble(next());
    }
    public final void close() {
        try {
            in.close();
        } catch (java.io.IOException e) {
            throw new java.io.UncheckedIOException(e);
        }
    }

    private static final class ByteBuffer {
        private static final int DEFAULT_BUF_SIZE = 1 << 12;
        private byte[] buf;
        private int ptr = 0;
        private ByteBuffer(int capacity) {
            this.buf = new byte[capacity];
        }
        private ByteBuffer() {
            this(DEFAULT_BUF_SIZE);
        }
        private ByteBuffer append(int b) {
            if (ptr == buf.length) {
                int newLength = buf.length << 1;
                byte[] newBuf = new byte[newLength];
                System.arraycopy(buf, 0, newBuf, 0, buf.length);
                buf = newBuf;
            }
            buf[ptr++] = (byte) b;
            return this;
        }
        private char[] toCharArray() {
            char[] chs = new char[ptr];
            for (int i = 0; i < ptr; i++) {
                chs[i] = (char) buf[i];
            }
            return chs;
        }
        private byte[] getRawBuf() {
            return buf;
        }
        private int size() {
            return ptr;
        }
        private void clear() {
            ptr = 0;
        }
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class ExtendedScanner extends FastScanner {
    public ExtendedScanner() {super();}
    public ExtendedScanner(InputStream in) {super(in);}
    public int[] ints(final int n) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> nextInt());
        return a;
    }
    public int[] ints(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
        return a;
    }
    public int[][] ints(final int n, final int m) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m));
        return a;
    }
    public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m, f));
        return a;
    }
    public long[] longs(final int n) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> nextLong());
        return a;
    }
    public long[] longs(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
        return a;
    }
    public long[][] longs(final int n, final int m) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m));
        return a;
    }
    public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m, f));
        return a;
    }
    public char[][] charArrays(final int n) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars());
        return c;
    }
    public double[] doubles(final int n) {
        final double[] a = new double[n];
        Arrays.setAll(a, $ -> nextDouble());
        return a;
    }
    public double[][] doubles(final int n, final int m) {
        final double[][] a = new double[n][];
        Arrays.setAll(a, $ -> doubles(m));
        return a;
    }
    public String[] strings(final int n) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next());
        return s;
    }
}


final class ModArithmetic998244353 extends ModArithmetic {
    public static final ModArithmetic INSTANCE = new ModArithmetic998244353();
    private ModArithmetic998244353(){}
    public static final long MOD = Const.MOD998244353;
    public long getMod() {return MOD;}
    public long mod(long a) {return (a %= MOD) < 0 ? a + MOD : a;}
    public long add(long a, long b) {return (a += b) >= MOD ? a - MOD : a;}
    public long sub(long a, long b) {return (a -= b) < 0 ? a + MOD : a;}
    public long mul(long a, long b) {return (a * b) % MOD;}
}

/**
 * @author https://atcoder.jp/users/suisen
 */
class FastPrintStream implements AutoCloseable {
    private static final int INT_MAX_LEN = 11;
    private static final int LONG_MAX_LEN = 20;

    private int precision = 9;

    private static final int BUF_SIZE = 1 << 14;
    private static final int BUF_SIZE_MINUS_INT_MAX_LEN = BUF_SIZE - INT_MAX_LEN;
    private static final int BUF_SIZE_MINUS_LONG_MAX_LEN = BUF_SIZE - LONG_MAX_LEN;
    private final byte[] buf = new byte[BUF_SIZE];
    private int ptr = 0;
    private final java.lang.reflect.Field strField;
    private final java.nio.charset.CharsetEncoder encoder;

    private final java.io.OutputStream out;

    public FastPrintStream(java.io.OutputStream out) {
        this.out = out;
        java.lang.reflect.Field f;
        try {
            f = java.lang.String.class.getDeclaredField("value");
            f.setAccessible(true);
        } catch (NoSuchFieldException | SecurityException e) {
            f = null;
        }
        this.strField = f;
        this.encoder = java.nio.charset.StandardCharsets.US_ASCII.newEncoder();
    }

    public FastPrintStream(java.io.File file) throws java.io.IOException {
        this(new java.io.FileOutputStream(file));
    }

    public FastPrintStream(java.lang.String filename) throws java.io.IOException {
        this(new java.io.File(filename));
    }

    public FastPrintStream() {
        this(new java.io.FileOutputStream(java.io.FileDescriptor.out));
    }

    public FastPrintStream println() {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) '\n';
        return this;
    }

    public FastPrintStream println(java.lang.Object o) {
        return print(o).println();
    }

    public FastPrintStream println(java.lang.String s) {
        return print(s).println();
    }

    public FastPrintStream println(char[] s) {
        return print(s).println();
    }

    public FastPrintStream println(char c) {
        return print(c).println();
    }

    public FastPrintStream println(int x) {
        return print(x).println();
    }

    public FastPrintStream println(long x) {
        return print(x).println();
    }

    public FastPrintStream println(double d, int precision) {
        return print(d, precision).println();
    }

    public FastPrintStream println(double d) {
        return print(d).println();
    }

    private FastPrintStream print(byte[] bytes) {
        int n = bytes.length;
        if (ptr + n > BUF_SIZE) {
            internalFlush();
            try {
                out.write(bytes);
            } catch (java.io.IOException e) {
                throw new java.io.UncheckedIOException(e);
            }
        } else {
            System.arraycopy(bytes, 0, buf, ptr, n);
            ptr += n;
        }
        return this;
    }

    public FastPrintStream print(java.lang.Object o) {
        return print(o.toString());
    }

    public FastPrintStream print(java.lang.String s) {
        if (strField == null) {
            return print(s.getBytes());
        } else {
            try {
                Object value = strField.get(s);
                if (value instanceof byte[]) {
                    return print((byte[]) value);
                } else {
                    return print((char[]) value);
                }
            } catch (IllegalAccessException e) {
                return print(s.getBytes());
            }
        }
    }

    public FastPrintStream print(char[] s) {
        try {
            return print(encoder.encode(java.nio.CharBuffer.wrap(s)).array());
        } catch (java.nio.charset.CharacterCodingException e) {
            byte[] bytes = new byte[s.length];
            for (int i = 0; i < s.length; i++) {
                bytes[i] = (byte) s[i];
            }
            return print(bytes);
        }
    }

    public FastPrintStream print(char c) {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) c;
        return this;
    }

    public FastPrintStream print(int x) {
        if (ptr > BUF_SIZE_MINUS_INT_MAX_LEN) internalFlush();
        if (-10 < x && x < 10) {
            if (x < 0) {
                buf[ptr++] = '-';
                x = -x;
            }
            buf[ptr++] = (byte) ('0' + x);
            return this;
        }
        int d;
        if (x < 0) {
            if (x == Integer.MIN_VALUE) {
                buf[ptr++] = '-'; buf[ptr++] = '2'; buf[ptr++] = '1'; buf[ptr++] = '4';
                buf[ptr++] = '7'; buf[ptr++] = '4'; buf[ptr++] = '8'; buf[ptr++] = '3';
                buf[ptr++] = '6'; buf[ptr++] = '4'; buf[ptr++] = '8';
                return this;
            }
            d = len(x = -x);
            buf[ptr++] = '-';
        } else {
            d = len(x);
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(long x) {
        if ((int) x == x) return print((int) x);
        if (ptr > BUF_SIZE_MINUS_LONG_MAX_LEN) internalFlush();
        int d;
        if (x < 0) {
            if (x == Long.MIN_VALUE) {
                buf[ptr++] = '-'; buf[ptr++] = '9'; buf[ptr++] = '2'; buf[ptr++] = '2';
                buf[ptr++] = '3'; buf[ptr++] = '3'; buf[ptr++] = '7'; buf[ptr++] = '2';
                buf[ptr++] = '0'; buf[ptr++] = '3'; buf[ptr++] = '6'; buf[ptr++] = '8';
                buf[ptr++] = '5'; buf[ptr++] = '4'; buf[ptr++] = '7'; buf[ptr++] = '7';
                buf[ptr++] = '5'; buf[ptr++] = '8'; buf[ptr++] = '0'; buf[ptr++] = '8';
                return this;
            }
            d = len(x = -x);
            buf[ptr++] = '-';
        } else {
            d = len(x);
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(double d, int precision) {
        if (d < 0) {
            print('-');
            d = -d;
        }
        d += Math.pow(10, -precision) / 2;
        print((long) d).print('.');
        d -= (long) d;
        for(int i = 0; i < precision; i++){
            d *= 10;
            print((int) d);
            d -= (int) d;
        }
        return this;
    }

    public FastPrintStream print(double d) {
        return print(d, precision);
    }

    public void setPrecision(int precision) {
        this.precision = precision;
    }

    private void internalFlush() {
        try {
            out.write(buf, 0, ptr);
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new java.io.UncheckedIOException(e);
        }
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new java.io.UncheckedIOException(e);
        }
    }

    public void close() {
        try {
            out.close();
        } catch (java.io.IOException e) {
            throw new java.io.UncheckedIOException(e);
        }
    }

    private static int len(int x) {
        return
            x >= 1000000000 ? 10 :
            x >= 100000000  ?  9 :
            x >= 10000000   ?  8 :
            x >= 1000000    ?  7 :
            x >= 100000     ?  6 :
            x >= 10000      ?  5 :
            x >= 1000       ?  4 :
            x >= 100        ?  3 :
            x >= 10         ?  2 : 1;
    }

    private static int len(long x) {
        return
            x >= 1000000000000000000l ? 19 :
            x >= 100000000000000000l  ? 18 :
            x >= 10000000000000000l   ? 17 :
            x >= 1000000000000000l    ? 16 :
            x >= 100000000000000l     ? 15 :
            x >= 10000000000000l      ? 14 :
            x >= 1000000000000l       ? 13 :
            x >= 100000000000l        ? 12 :
            x >= 10000000000l         ? 11 : 10;
    }
}

class Const {
    public static final long   LINF   = 1l << 59;
    public static final int    IINF   = (1  << 30) - 1;
    public static final double DINF   = 1e150;
    
    public static final double SMALL  = 1e-12;
    public static final double MEDIUM = 1e-9;
    public static final double LARGE  = 1e-6;

    public static final long MOD1000000007 = 1000000007;
    public static final long MOD998244353  = 998244353 ;
    public static final long MOD754974721  = 754974721 ;
    public static final long MOD167772161  = 167772161 ;
    public static final long MOD469762049  = 469762049 ;

    public static final int[] dx8 = {1, 0, -1, 0, 1, -1, -1, 1};
    public static final int[] dy8 = {0, 1, 0, -1, 1, 1, -1, -1};
    public static final int[] dx4 = {1, 0, -1, 0};
    public static final int[] dy4 = {0, 1, 0, -1};
}

/**
 * @author https://atcoder.jp/users/suisen
 */
abstract class ModArithmetic {
    public abstract long getMod();
    public abstract long mod(long a);
    public abstract long add(long a, long b);
    public abstract long sub(long a, long b);
    public abstract long mul(long a, long b);
    public final long div(long a, long b) {return mul(a, inv(b));}
    public final long inv(long a) {
        a = mod(a);
        long b = getMod();
        long u = 1, v = 0;
        while (b >= 1) {
            long t = a / b;
            a -= t * b;
            long tmp1 = a; a = b; b = tmp1;
            u -= t * v;
            long tmp2 = u; u = v; v = tmp2;
        }
        if (a != 1) throw new ArithmeticException("divide by zero");
        return mod(u);
    }
    public final long fma(long a, long b, long c) {return add(mul(a, b), c);}
    public final long pow(long a, long b) {
        long pow = 1;
        for (a = mod(a); b > 0; b >>= 1, a = mul(a, a)) {
            if ((b & 1) == 1) pow = mul(pow, a);
        }
        return pow;
    }

    public final long add(long a, long b, long c) {return mod(a + b + c);}
    public final long add(long a, long b, long c, long d) {return mod(a + b + c + d);}
    public final long add(long a, long b, long c, long d, long e) {return mod(a + b + c + d + e);}
    public final long add(long a, long b, long c, long d, long e, long f) {return mod(a + b + c + d + e + f);}
    public final long add(long a, long b, long c, long d, long e, long f, long g) {return mod(a + b + c + d + e + f + g);}
    public final long add(long a, long b, long c, long d, long e, long f, long g, long h) {return mod(a + b + c + d + e + f + g + h);}
    public final long add(long... xs) {long s = 0; for (long x : xs) s += x; return mod(s);}
    public final long mul(long a, long b, long c) {return mul(a, mul(b, c));}
    public final long mul(long a, long b, long c, long d) {return mul(a, mul(b, mul(c, d)));}
    public final long mul(long a, long b, long c, long d, long e) {return mul(a, mul(b, mul(c, mul(d, e))));}
    public final long mul(long a, long b, long c, long d, long e, long f) {return mul(a, mul(b, mul(c, mul(d, mul(e, f)))));}
    public final long mul(long a, long b, long c, long d, long e, long f, long g) {return mul(a, mul(b, mul(c, mul(d, mul(e, mul(f, g))))));}
    public final long mul(long a, long b, long c, long d, long e, long f, long g, long h) {return mul(a, mul(b, mul(c, mul(d, mul(e, mul(f, mul(g, h)))))));}
    public final long mul(long... xs) {long s = 1; for (long x : xs) s = mul(s, x); return s;}
    public final java.util.OptionalLong sqrt(long a) {
        a = mod(a);
        if (a == 0) return java.util.OptionalLong.of(0);
        if (a == 1) return java.util.OptionalLong.of(1);
        long p = getMod();
        if (pow(a, (p - 1) >> 1) != 1) {
            return java.util.OptionalLong.empty();
        }
        if ((p & 3) == 3) {
            return java.util.OptionalLong.of(pow(a, (p + 1) >> 2));
        }
        if ((p & 7) == 5) {
            if (pow(a, (p - 1) >> 2) == 1) {
                return java.util.OptionalLong.of(pow(a, (p + 3) >> 3));
            } else {
                return java.util.OptionalLong.of(mul(pow(2, (p - 1) >> 2), pow(a, (p + 3) >> 3)));
            }
        }
        long S = 0, Q = p - 1;
        while ((Q & 1) == 0) {
            ++S;
            Q >>= 1;
        }
        long z = 1;
        while (pow(z, (p - 1) >> 1) != p - 1) ++z;
        long c = pow(z, Q), R = pow(a, (Q + 1) / 2), t = pow(a, Q), M = S;
        while (t != 1) {
            long cur = t;
            int i;
            for (i = 1; i < M; i++) {
                cur = mul(cur, cur);
                if (cur == 1) break;
            }
            long b = pow(c, 1l << (M - i - 1));
            c = mul(b, b); R = mul(R, b); t = mul(t, b, b); M = i;
        }
        return java.util.OptionalLong.of(R);
    }

    /** array operations */

    public final long[] rangeInv(int n) {
        final long MOD = getMod();
        long[] invs = new long[n + 1];
        if (n == 0) return invs;
        invs[1] = 1;
        for (int i = 2; i <= n; i++) {
            invs[i] = mul(MOD - MOD / i, invs[(int) (MOD % i)]);
        }
        return invs;
    }
    public final long[] arrayInv(long[] a) {
        int n = a.length;
        long[] l = new long[n + 1];
        long[] r = new long[n + 1];
        l[0] = r[n] = 1;
        for (int i = 0; i < n; i++) l[i + 1] = mul(l[i], a[i    ]);
        for (int i = n; i > 0; i--) r[i - 1] = mul(r[i], a[i - 1]);
        long invAll = inv(l[n]);
        long[] invs = new long[n];
        for (int i = 0; i < n; i++) {
            invs[i] = mul(l[i], r[i + 1], invAll);
        }
        return invs;
    }
    public final long[] factorial(int n) {
        long[] ret = new long[n + 1];
        ret[0] = 1;
        for (int i = 1; i <= n; i++) ret[i] = mul(ret[i - 1], i);
        return ret;
    }
    public final long[] factorialInv(int n) {
        long facN = 1;
        for (int i = 2; i <= n; i++) facN = mul(facN, i);
        long[] invs = new long[n + 1];
        invs[n] = inv(facN);
        for (int i = n; i > 0; i--) invs[i - 1] = mul(invs[i], i);
        return invs;
    }
    public final long[] rangePower(long a, int n) {
        a = mod(a);
        long[] pows = new long[n + 1];
        pows[0] = 1;
        for (int i = 1; i <= n; i++) pows[i] = mul(pows[i - 1], a);
        return pows;
    }
    public final long[] rangePowerInv(long a, int n) {
        a = mod(a);
        long[] invs = new long[n + 1];
        invs[n] = inv(pow(a, n));
        for (int i = n; i > 0; i--) invs[i - 1] = mul(invs[i], a);
        return invs;
    }

    /** combinatric operations */

    public final long[][] combTable(int n) {
        long[][] comb = new long[n + 1][];
        for (int i = 0; i <= n; i++) {
            comb[i] = new long[i + 1];
            comb[i][0] = comb[i][i] = 1;
            for (int j = 1; j < i; j++) {
                comb[i][j] = add(comb[i - 1][j - 1], comb[i - 1][j]);
            }
        }
        return comb;
    }
    public final long comb(int n, int r, long[] fac, long[] facInv) {
        return r < 0 || r > n ? 0 : mul(fac[n], facInv[r], facInv[n - r]);
    }
    public final long naiveComb(long n, long r) {
        if (r < 0 || r > n) return 0;
        r = Math.min(r, n - r);
        long num = 1, den = 1;
        for (int i = 0; i < r; i++) {
            num = mul(num, n - i);
            den = mul(den, i + 1);
        }
        return div(num, den);
    }
    public final long perm(int n, int r, long[] fac, long[] facInv) {
        return r < 0 || r > n ? 0 : mul(fac[n], facInv[n - r]);
    }
    public final long naivePerm(long n, long r) {
        if (r < 0 || r > n) return 0;
        long res = 1;
        for (long i = 0; i < r; i++) res = mul(res, n - i);
        return res;
    }
}
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