結果
| 問題 |
No.856 増える演算
|
| コンテスト | |
| ユーザー |
 CuriousFairy315
|
| 提出日時 | 2019-07-08 03:56:04 |
| 言語 | Java (openjdk 23) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 43,622 bytes |
| コンパイル時間 | 4,240 ms |
| コンパイル使用メモリ | 99,212 KB |
| 実行使用メモリ | 161,036 KB |
| 最終ジャッジ日時 | 2024-10-09 16:08:46 |
| 合計ジャッジ時間 | 131,112 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 57 WA * 23 |
ソースコード
import java.awt.Point;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.Serializable;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Iterator;
import java.util.Locale;
import java.util.NoSuchElementException;
import java.util.function.UnaryOperator;
public class Main {
public static void main(String[] args) {
new Main();
}
private class Pair implements Comparable<Pair>{
int first, second;
Pair(int i, int j) {
first = i;
second = j;
}
private double comp() {
return Math.log(first + second) + second * Math.log(first);
}
@Override
public int compareTo(Pair o) {
return Double.compare(comp(), o.comp());
}
}
public Main() {
FastIO io = new FastIO();
int[] A = io.nextInt(io.nextInt());
ModUtility mod = new ModUtility(1000000007);
if (!IntRange.closed(2, 100000).contains(A.length)) System.exit(1);
for (int i : A) if (!IntRange.closed(1, 100000).contains(i)) System.exit(1);
Pair minimum = new Pair(A[A.length - 2], A[A.length - 1]); // これが最小の要素、つまり分母
for (int i = A.length - 2, min = A[A.length - 1];i >= 0;min = Math.min(min, A[i--])) {
Pair tmp = new Pair(A[i], min);
minimum = minimum.compareTo(tmp) <= 0 ? minimum : tmp;
}
ModInteger ans = mod.create(1);
ans.divideEqual(mod.multiply(minimum.first + minimum.second, mod.pow(minimum.first, minimum.second))); // 分母を割る
for (int i = A.length - 1, sum = 0;i >= 0;sum += A[i--]) ans.multiplyEqual(mod.pow(A[i], sum)); // まず指数部を全部掛ける
int[] bucket = new int[100001];
Arrays.fill(bucket, 0);
for (int i : A) ++ bucket[i];
long[] fft = convolute(bucket, bucket); // FFTでA_i+A_jを求める
for (int i : IntRange.closed(2, 200000)) {
if (i % 2 != 0) fft[i] -= bucket[i / 2];
fft[i] /= 2;
ans.multiplyEqual(mod.pow(i - 1, (int)fft[i])); // それぞれの和を掛ける
}
io.println(ans);
io.flush();
}
private long[] convolute(int[] a, int[] b) {
int N = a.length;
int M = Integer.highestOneBit(Math.max(a.length, b.length) + 1) << 2;
Complex[] ca = new Complex[M];
Complex[] cb = new Complex[M];
for (int i = 0; i < M; i++) {
ca[i] = new Complex(0, 0);
cb[i] = new Complex(0, 0);
}
for (int i = 0; i < N; i++) {
ca[i + 1].real = a[i];
cb[i + 1].real = b[i];
}
Complex[] cret = multipy(M, ca, cb);
long[] ret = new long[M - 1];
for (int i = 0; i < ret.length; i++) {
ret[i] = Math.round(cret[i + 1].real);
}
return ret;
}
public Complex[] multipy(int n, Complex[] g, Complex[] h) {
Complex[] gg = FFT(g, n, false);
Complex[] hh = FFT(h, n, false);
Complex[] ff = new Complex[n];
for (int i = 0; i < n; i++) {
ff[i] = gg[i].multiply(hh[i]);
}
ff = FFT(ff, n, true);
for (int i = 0; i < n; i++) {
ff[i] = ff[i].multiply(1.0 / n);
}
return ff;
}
private Complex[] FFT(Complex[] f, int n, boolean inv) {
if (n == 1) {
return new Complex[] { f[0] };
}
Complex[] f0 = new Complex[n / 2];
Complex[] f1 = new Complex[n / 2];
for (int i = 0; i < n / 2; i++) {
f0[i] = f[2 * i + 0];
f1[i] = f[2 * i + 1];
}
f0 = FFT(f0, n / 2, inv);
f1 = FFT(f1, n / 2, inv);
Complex zeta = new Complex(Math.cos(2 * Math.PI / n), Math.sin(2 * Math.PI / n));
Complex pow_zeta = new Complex(1.0, 0);
Complex[] ret = new Complex[n];
for (int i = 0; i < n; i++) {
if (inv) {
ret[i] = f0[i % (n / 2)].add(f1[i % (n / 2)].divide(pow_zeta));
} else {
ret[i] = f0[i % (n / 2)].add(f1[i % (n / 2)].multiply(pow_zeta));
}
pow_zeta = pow_zeta.multiply(zeta);
}
return ret;
}
public class Complex {
double real, img;
public Complex(double real, double img) {
this.real = real;
this.img = img;
}
public Complex add(Complex c) {
return new Complex(this.real + c.real, this.img + c.img);
}
public Complex multiply(double d) {
return new Complex(this.real * d, this.img * d);
}
public Complex multiply(Complex c) {
double real = this.real * c.real - this.img * c.img;
double img = this.real * c.img + this.img * c.real;
return new Complex(real, img);
}
public Complex divide(Complex c) {
double real = this.real * c.real + this.img * c.img;
double img = -this.real * c.img + this.img * c.real;
Complex divide = new Complex(real, img);
return divide.multiply(1.0 / (c.real * c.real + c.img * c.img));
}
public String toString() {
return this.real + " + " + this.img + "i";
}
}
public class FastIO {
private final InputStream in = System.in;
private final byte[] buffer = new byte[1024];
private int read = 0;
private int length = 0;
public final PrintWriter out = new PrintWriter(System.out, false);
public final PrintWriter err = new PrintWriter(System.err, false);
private boolean hasNextByte() {
if (read < length) return true;
read = 0;
try {
length = in.read(buffer);
} catch (IOException e) {
e.printStackTrace();
}
return length > 0;
}
private int readByte() {
return hasNextByte() ? buffer[read++] : -1;
}
private boolean isPrintableChar(int c) {
return 33 <= c && c <= 126;
}
private boolean isNumber(int c) {
return '0' <= c && c <= '9';
}
public boolean hasNext() {
while (hasNextByte() && !isPrintableChar(buffer[read])) read++;
return hasNextByte();
}
public char nextChar() {
if (!hasNextByte()) throw new NoSuchElementException();
return (char)readByte();
}
public char[][] nextChar(int height) {
char[][] ret = new char[height][];
for (int i = 0;i < ret.length;++ i) ret[i] = next().toCharArray();
return ret;
}
public String next() {
if (!hasNext()) throw new NoSuchElementException();
StringBuilder sb = new StringBuilder();
int b;
while (isPrintableChar(b = readByte())) sb.appendCodePoint(b);
return sb.toString();
}
public long nextLong() {
if (!hasNext()) throw new NoSuchElementException();
long n = 0;
boolean minus = false;
int b = readByte();
if (b == '-') {
minus = true;
b = readByte();
}
if (!isNumber(b)) throw new NumberFormatException();
while (true) {
if (isNumber(b)) {
n *= 10;
n += b - '0';
} else if (b == -1 || !isPrintableChar(b)) return minus ? -n : n;
else throw new NumberFormatException();
b = readByte();
}
}
public int nextInt() {
long nl = nextLong();
if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
return (int) nl;
}
public double nextDouble() {
return Double.parseDouble(next());
}
public int[] nextInt(int width) {
int[] ret = new int[width];
for (int i = 0;i < width;++ i) ret[i] = nextInt();
return ret;
}
public long[] nextLong(int width) {
long[] ret = new long[width];
for (int i = 0;i < width;++ i) ret[i] = nextLong();
return ret;
}
public int[][] nextInt(int width, int height) {
int[][] ret = new int[height][width];
for (int i = 0, j;i < height;++ i) for (j = 0;j < width;++ j) ret[i][j] = nextInt();
return ret;
}
public long[][] nextLong(int width, int height) {
long[][] ret = new long[height][width];
for (int i = 0, j;i < height;++ i) for (j = 0;j < width;++ j) ret[j][i] = nextLong();
return ret;
}
public boolean[] nextBoolean(char T) {
char[] s = next().toCharArray();
boolean[] ret = new boolean[s.length];
for (int i = 0;i < ret.length;++ i) ret[i] = s[i] == T;
return ret;
}
public boolean[][] nextBoolean(char T, int height) {
boolean[][] ret = new boolean[height][];
for (int i = 0;i < ret.length;++ i) {
char[] s = next().toCharArray();
ret[i] = new boolean[s.length];
for (int j = 0;j < ret[i].length;++ j) ret[i][j] = s[j] == T;
}
return ret;
}
public Point nextPoint() {
return new Point(nextInt(), nextInt());
}
public Point[] nextPoint(int width) {
Point[] ret = new Point[width];
for (int i = 0;i < width;++ i) ret[i] = nextPoint();
return ret;
}
@Override
protected void finalize() throws Throwable {
try {
super.finalize();
} finally {
in.close();
out.close();
err.close();
}
}
public void print(boolean b) {
out.print(b);
}
public void print(char c) {
out.print(c);
}
public void print(char[] s) {
out.print(s);
}
public void print(double d) {
out.print(d);
}
public void print(double d, int length) {
if (d < 0) {
out.print('-');
d = -d;
}
d += Math.pow(10, -length) / 2;
out.print((long)d);
out.print('.');
d -= (long)d;
for (int i = 0;i < length;++ i) {
d *= 10;
out.print((int)d);
d -= (int)d;
}
}
public void print(float f) {
out.print(f);
}
public void print(int i) {
out.print(i);
}
public void print(long l) {
out.print(l);
}
public void print(Object obj) {
out.print(obj);
}
public void print(String s) {
out.print(s);
}
public void print(Object[] obj, String perse) {
print(obj[0]);
for (int i = 1;i < obj.length;++ i) {
print(perse);
print(obj[i]);
}
}
public void print(Object[][] obj, String perse1, String perse2) {
print(obj[0], perse1);
for (int i = 1;i < obj.length;++ i) {
print(perse2);
print(obj[i], perse1);
}
}
public void printf(String format, Object... args) {
out.printf(format, args);
}
public void printf(Locale l, String format, Object... args) {
out.printf(l, format, args);
}
public void println() {
out.println();
}
public void println(boolean b) {
out.println(b);
}
public void println(char c) {
out.println(c);
}
public void println(char[] s) {
out.println(s);
}
public void println(double d) {
out.println(d);
}
public void println(double d, int length) {
print(d, length);
println();
}
public void println(float f) {
out.println(f);
}
public void println(int i) {
out.println(i);
}
public void println(long l) {
out.println(l);
}
public void println(Object obj) {
out.println(obj);
}
public void println(String s) {
out.println(s);
}
public void println(Object[] obj, String perse) {
print(obj, perse);
println();
}
public void println(Object[][] obj, String perse1, String perse2) {
print(obj, perse1, perse2);
println();
}
public void flush() {
out.flush();
err.flush();
}
}
public enum BoundType {
CLOSED, OPEN;
}
public static class Range<C> implements Serializable{
private static final long serialVersionUID = -4702828934863023392L;
protected C lower;
protected C upper;
protected BoundType lowerType;
protected BoundType upperType;
private Comparator<? super C> comparator;
protected Range(C lower, BoundType lowerType, C upper, BoundType upperType) {
this(lower, lowerType, upper, upperType, null);
}
protected Range(C lower, BoundType lowerType, C upper, BoundType upperType, Comparator<? super C> comparator) {
this.lower = lower;
this.upper = upper;
this.lowerType = lowerType;
this.upperType = upperType;
this.comparator = comparator;
}
public static <C extends Comparable<? super C>> Range<C> range(C lower, BoundType lowerType, C upper, BoundType upperType) {
if (lower != null && upper != null) {
int comp = lower.compareTo(upper);
if (comp > 0) return new Range<C>(null, BoundType.CLOSED, null, BoundType.CLOSED);
else if (comp == 0 && (lowerType == BoundType.OPEN || upperType == BoundType.OPEN))return new Range<C>(null, BoundType.CLOSED, null, BoundType.CLOSED);
}
return new Range<C>(lower, lowerType, upper, upperType);
}
public static <C> Range<C> range(C lower, BoundType lowerType, C upper, BoundType upperType, Comparator<? super C> comparator) {
if (lower != null && upper != null) {
int comp = comparator.compare(lower, upper);
if (comp > 0) return new Range<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, comparator);
else if (comp == 0 && (lowerType == BoundType.OPEN || upperType == BoundType.OPEN)) return new Range<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, comparator);
}
return new Range<C>(lower, lowerType, upper, upperType, comparator);
}
public static <C extends Comparable<? super C>> Range<C> all() {
return range(null, BoundType.OPEN, null, BoundType.OPEN);
}
public static <C> Range<C> all(Comparator<? super C> comparator) {
return range(null, BoundType.OPEN, null, BoundType.OPEN, comparator);
}
public static <C extends Comparable<? super C>> Range<C> atMost(C upper) {
return range(null, BoundType.OPEN, upper, BoundType.CLOSED);
}
public static <C> Range<C> atMost(C upper, Comparator<? super C> comparator) {
return range(null, BoundType.OPEN, upper, BoundType.CLOSED, comparator);
}
public static <C extends Comparable<? super C>> Range<C> lessThan(C upper) {
return range(null, BoundType.OPEN, upper, BoundType.OPEN);
}
public static <C> Range<C> lessThan(C upper, Comparator<? super C> comparator) {
return range(null, BoundType.OPEN, upper, BoundType.OPEN, comparator);
}
public static <C extends Comparable<? super C>> Range<C> downTo(C upper, BoundType boundType) {
return range(null, BoundType.OPEN, upper, boundType);
}
public static <C> Range<C> downTo(C upper, BoundType boundType, Comparator<? super C> comparator) {
return range(null, BoundType.OPEN, upper, boundType, comparator);
}
public static <C extends Comparable<? super C>> Range<C> atLeast(C lower) {
return range(lower, BoundType.CLOSED, null, BoundType.OPEN);
}
public static <C> Range<C> atLeast(C lower, Comparator<? super C> comparator) {
return range(lower, BoundType.CLOSED, null, BoundType.OPEN, comparator);
}
public static <C extends Comparable<? super C>> Range<C> greaterThan(C lower) {
return range(lower, BoundType.OPEN, null, BoundType.OPEN);
}
public static <C> Range<C> greaterThan(C lower, Comparator<? super C> comparator) {
return range(lower, BoundType.OPEN, null, BoundType.OPEN, comparator);
}
public static <C extends Comparable<? super C>> Range<C> upTo(C lower, BoundType boundType) {
return range(lower, boundType, null, BoundType.OPEN);
}
public static <C> Range<C> upTo(C lower, BoundType boundType, Comparator<? super C> comparator) {
return range(lower, boundType, null, BoundType.OPEN, comparator );
}
public static <C extends Comparable<? super C>> Range<C> open(C lower, C upper) {
return range(lower, BoundType.OPEN, upper, BoundType.OPEN);
}
public static <C> Range<C> open(C lower, C upper, Comparator<? super C> comparator) {
return range(lower, BoundType.OPEN, upper, BoundType.OPEN, comparator);
}
public static <C extends Comparable<? super C>> Range<C> openClosed(C lower, C upper) {
return range(lower, BoundType.OPEN, upper, BoundType.CLOSED);
}
public static <C> Range<C> openClosed(C lower, C upper, Comparator<? super C> comparator) {
return range(lower, BoundType.OPEN, upper, BoundType.CLOSED, comparator);
}
public static <C extends Comparable<? super C>> Range<C> closedOpen(C lower, C upper) {
return range(lower, BoundType.CLOSED, upper, BoundType.OPEN);
}
public static <C> Range<C> closedOpen(C lower, C upper, Comparator<? super C> comparator) {
return range(lower, BoundType.CLOSED, upper, BoundType.OPEN, comparator);
}
public static <C extends Comparable<? super C>> Range<C> closed(C lower, C upper) {
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED);
}
public static <C> Range<C> closed(C lower, C upper, Comparator<? super C> comparator) {
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED, comparator);
}
public static <C extends Comparable<? super C>> Range<C> singleton(C value) {
return range(value, BoundType.CLOSED, value, BoundType.CLOSED);
}
public static <C> Range<C> singleton(C value, Comparator<? super C> comparator) {
return range(value, BoundType.CLOSED, value, BoundType.CLOSED, comparator);
}
public static <C extends Comparable<? super C>> Range<C> empty() {
return range(null, BoundType.CLOSED, null, BoundType.CLOSED);
}
public static <C> Range<C> empty(Comparator<? super C> comparator) {
return range(null, BoundType.CLOSED, null, BoundType.CLOSED, comparator);
}
public static <C extends Comparable<? super C>> Range<C> encloseAll(Iterable<C> values) {
C lower = values.iterator().next();
C upper = lower;
for (C i : values) {
if (lower.compareTo(i) > 0) lower = i;
if (upper.compareTo(i) < 0) upper = i;
}
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED);
}
public static <C> Range<C> encloseAll(Iterable<C> values, Comparator<? super C> comparator) {
C lower = values.iterator().next();
C upper = lower;
for (C i : values) {
if (comparator.compare(lower, i) > 0) lower = i;
if (comparator.compare(upper, i) < 0) upper = i;
}
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED, comparator);
}
protected int compareLower(C value) {
return compareLower(value, BoundType.CLOSED);
}
protected int compareLower(C value, BoundType boundType) {
return compareLower(lower, lowerType, value, boundType);
}
protected int compareLower(C lower, BoundType lowerType, C value) {
return compareLower(lower, lowerType, value, BoundType.CLOSED);
}
protected int compareLower(C lower, BoundType lowerType, C value, BoundType boundType) {
if (lower == null) return value == null ? 0 : -1;
else if (value == null) return 1;
int compare;
if (comparator == null) {
@SuppressWarnings("unchecked")
Comparable<C> comp = (Comparable<C>)lower;
compare = comp.compareTo(value);
} else compare = comparator.compare(lower, value);
if (compare == 0) {
if (lowerType == BoundType.CLOSED) -- compare;
if (boundType == BoundType.CLOSED) ++ compare;
}
return compare;
}
protected int compareUpper(C value) {
return compareUpper(value, BoundType.CLOSED);
}
protected int compareUpper(C value, BoundType boundType) {
return compareUpper(upper, upperType, value, boundType);
}
protected int compareUpper(C upper, BoundType upperType, C value) {
return compareUpper(upper, upperType, value, BoundType.CLOSED);
}
protected int compareUpper(C upper, BoundType upperType, C value, BoundType boundType) {
if (upper == null) return value == null ? 0 : 1;
if (value == null) return -1;
int compare;
if (comparator == null) {
@SuppressWarnings("unchecked")
Comparable<C> comp = (Comparable<C>)upper;
compare = comp.compareTo(value);
} else compare = comparator.compare(upper, value);
if (compare == 0) {
if (upperType == BoundType.CLOSED) ++ compare;
if (boundType == BoundType.CLOSED) -- compare;
}
return compare;
}
public boolean hasLowerBound() {
return lower != null;
}
public C lowerEndpoint() {
if (hasLowerBound()) return lower;
throw new IllegalStateException();
}
public BoundType lowerBoundType() {
if (hasLowerBound()) return lowerType;
throw new IllegalStateException();
}
public boolean hasUpperBound() {
return upper != null;
}
public C upperEndpoint() {
if (hasUpperBound()) return upper;
throw new IllegalStateException();
}
public BoundType upperBoundType() {
if (hasUpperBound()) return upperType;
throw new IllegalStateException();
}
/**
* この区間が空集合か判定します。
* @return 空集合ならばtrue
*/
public boolean isEmpty() {
return lower == null && upper == null && lowerType == BoundType.CLOSED;
}
/**
* 与えられた引数が区間の左側に位置するか判定します。<br>
* 接する場合は区間の左側ではないと判定します。
* @param value 調べる引数
* @return 区間の左側に位置するならtrue
*/
public boolean isLess(C value) {
return isLess(value, BoundType.CLOSED);
}
protected boolean isLess(C value, BoundType boundType) {
return compareLower(value, boundType) > 0;
}
/**
* 与えられた引数が区間の右側に位置するか判定します。<br>
* 接する場合は区間の右側ではないと判定します。
* @param value 調べる引数
* @return 区間の右側に位置するならtrue
*/
public boolean isGreater(C value) {
return isGreater(value, BoundType.CLOSED);
}
private boolean isGreater(C value, BoundType boundType) {
return compareUpper(value, boundType) < 0;
}
/**
* 与えられた引数が区間内に位置するか判定します。<br>
* 接する場合も区間内に位置すると判定します。
* @param value 調べる引数
* @return 区間内に位置するならtrue
*/
public boolean contains(C value) {
return !isLess(value) && !isGreater(value) && !isEmpty();
}
/**
* 与えられた引数すべてが区間内に位置するか判定します。<br>
* 接する場合も区間内に位置すると判定します。
* @param value 調べる要素
* @return 全ての要素が区間内に位置するならtrue
*/
public boolean containsAll(Iterable<? extends C> values) {
for (C i : values) if (!contains(i)) return false;
return true;
}
/**
* 与えられた区間がこの区間に内包されるか判定します。<br>
*
* @param other
* @return 与えられた区間がこの区間に内包されるならtrue
*/
public boolean encloses(Range<C> other) {
return !isLess(other.lower, other.lowerType) && !isGreater(other.upper, other.upperType);
}
/**
* 与えられた区間がこの区間と公差するか判定します。<br>
* 接する場合は公差するものとします。
* @param value 調べる引数
* @return 区間が交差するならtrue
*/
public boolean isConnected(Range<C> other) {
if (this.isEmpty() || other.isEmpty()) return false;
C lower, upper;
BoundType lowerType, upperType;
if (isLess(other.lower, other.lowerType)) {
lower = other.lower;
lowerType = other.lowerType;
} else {
lower = this.lower;
lowerType = this.lowerType;
}
if (isGreater(other.upper, other.upperType)) {
upper = other.upper;
upperType = other.upperType;
} else {
upper = this.upper;
upperType = this.upperType;
}
if (lower == null || upper == null) return true;
int comp = compareLower(lower, lowerType, upper, upperType);
return comp <= 0;
}
/**
* この区間との積集合を返します。
* @param connectedRange 積集合を求める区間
* @return 積集合
*/
public Range<C> intersection(Range<C> connectedRange) {
if (this.isEmpty() || connectedRange.isEmpty()) {
if (comparator == null) return new Range<C>(null, BoundType.CLOSED, null, BoundType.CLOSED);
return empty(comparator);
}
C lower, upper;
BoundType lowerType, upperType;
if (isLess(connectedRange.lower, connectedRange.lowerType)) {
lower = connectedRange.lower;
lowerType = connectedRange.lowerType;
} else {
lower = this.lower;
lowerType = this.lowerType;
}
if (isGreater(connectedRange.upper, connectedRange.upperType)) {
upper = connectedRange.upper;
upperType = connectedRange.upperType;
} else {
upper = this.upper;
upperType = this.upperType;
}
if (comparator == null) {
return new Range<C>(lower, lowerType, upper, upperType);
}
return range(lower, lowerType, upper, upperType, comparator);
}
/**
* この区間との和集合を返します。
* @param other 和集合を求める区間
* @return 和集合
*/
public Range<C> span(Range<C> other) {
if (other.isEmpty()) return new Range<C>(lower, lowerType, upper, upperType);
C lower, upper;
BoundType lowerType, upperType;
if (isLess(other.lower, other.lowerType)) {
lower = this.lower;
lowerType = this.lowerType;
} else {
lower = other.lower;
lowerType = other.lowerType;
}
if (isGreater(other.upper, other.upperType)) {
upper = this.upper;
upperType = this.upperType;
} else {
upper = other.upper;
upperType = other.upperType;
}
return new Range<C>(lower, lowerType, upper, upperType, comparator);
}
@Override
public boolean equals(Object object) {
if (this == object) return true;
if (object instanceof Range) {
@SuppressWarnings("unchecked")
Range<C> comp = (Range<C>) object;
return compareLower(comp.lower, comp.lowerType) == 0 && compareUpper(comp.upper, comp.upperType) == 0 && lowerType == comp.lowerType && upperType == comp.upperType;
}
return false;
}
@Override
public int hashCode() {
if (lower == null && upper == null) return 0;
else if (lower == null) return upper.hashCode();
else if (upper == null) return lower.hashCode();
return lower.hashCode() ^ upper.hashCode();
}
@Override
public String toString() {
if (isEmpty()) return "()";
return (lowerType == BoundType.OPEN ? "(" : "[") + (lower == null ? "" : lower.toString()) + ".." + (upper == null ? "" : upper.toString()) + (upperType == BoundType.OPEN ? ")" : "]");
}
}
public static class IterableRange<C> extends Range<C> implements Iterable<C>{
private static final long serialVersionUID = 9065915259748260688L;
protected UnaryOperator<C> func;
protected IterableRange(C lower, BoundType lowerType, C upper, BoundType upperType, UnaryOperator<C> func) {
super(lower, lowerType, upper, upperType);
this.func = func;
}
public static <C extends Comparable<? super C>> IterableRange<C> range(C lower, BoundType lowerType, C upper, BoundType upperType, UnaryOperator<C> func) {
if (lower == null || upper == null) return new IterableRange<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, func);
int comp = lower.compareTo(upper);
if (comp > 0) return new IterableRange<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, func);
else if (comp == 0 && (lowerType == BoundType.OPEN || upperType == BoundType.OPEN)) return new IterableRange<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, func);
return new IterableRange<C>(lower, lowerType, upper, upperType, func);
}
public static <C extends Comparable<? super C>> IterableRange<C> open(C lower, C upper, UnaryOperator<C> func) {
if (lower == null) return new IterableRange<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, func);
return range(func.apply(lower), BoundType.CLOSED, upper, BoundType.OPEN, func);
}
public static <C extends Comparable<? super C>> IterableRange<C> openClosed(C lower, C upper, UnaryOperator<C> func) {
if (lower == null) return new IterableRange<C>(null, BoundType.CLOSED, null, BoundType.CLOSED, func);
return range(func.apply(lower), BoundType.CLOSED, upper, BoundType.CLOSED, func);
}
public static <C extends Comparable<? super C>> IterableRange<C> closedOpen(C lower, C upper, UnaryOperator<C> func) {
return range(lower, BoundType.CLOSED, upper, BoundType.OPEN, func);
}
public static <C extends Comparable<? super C>> IterableRange<C> closed(C lower, C upper, UnaryOperator<C> func) {
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED, func);
}
public static <C extends Comparable<? super C>> IterableRange<C> singleton(C value, UnaryOperator<C> func) {
return range(value, BoundType.CLOSED, value, BoundType.CLOSED, func);
}
protected class Iter implements Iterator<C> {
C now;
Iter() {
now = lower;
}
@Override
public final boolean hasNext() {
return !isGreater(now);
}
@Override
public final C next() {
C ret = now;
now = func.apply(now);
return ret;
}
@Override
public final void remove() {
throw new UnsupportedOperationException();
}
}
protected class EmptyIter implements Iterator<C> {
@Override
public boolean hasNext() {
return false;
}
@Override
public C next() {
return null;
}
}
@Override
public Iterator<C> iterator() {
return lower == null || upper == null ? new EmptyIter() : new Iter();
}
public int getDistance() {
C check = upper;
int ret = 0;
while (lower != check) {
check = func.apply(check);
++ ret;
}
return ret;
}
}
public static class IntRange extends IterableRange<Integer>{
private static final long serialVersionUID = 5623995336491967216L;
private final boolean useFastIter;
private static class Next implements UnaryOperator<Integer> {
@Override
public Integer apply(Integer value) {
return value + 1;
}
}
protected IntRange() {
super(null, BoundType.CLOSED, null, BoundType.CLOSED, new Next());
useFastIter = true;
}
protected IntRange(UnaryOperator<Integer> func) {
super(null, BoundType.CLOSED, null, BoundType.CLOSED, func);
useFastIter = false;
}
protected IntRange(int lower, BoundType lowerType, int upper, BoundType upperType) {
super(lower, lowerType, upper, upperType, new Next());
useFastIter = true;
}
protected IntRange(int lower, BoundType lowerType, int upper, BoundType upperType, UnaryOperator<Integer> func) {
super(lower, lowerType, upper, upperType, func);
useFastIter = false;
}
public static IntRange range(int lower, BoundType lowerType, int upper, BoundType upperType) {
if (lower > upper) return new IntRange();
if (lowerType == BoundType.OPEN) ++ lower;
if (upperType == BoundType.OPEN) -- upper;
return new IntRange(lower, BoundType.CLOSED, upper, BoundType.CLOSED);
}
public static IntRange range(int lower, BoundType lowerType, int upper, BoundType upperType, UnaryOperator<Integer> func) {
if (lower > upper) return new IntRange(func);
if (lowerType == BoundType.OPEN) ++ lower;
if (upperType == BoundType.OPEN) -- upper;
return new IntRange(lower, BoundType.CLOSED, upper, BoundType.CLOSED, func);
}
public static IntRange open(int lower, int upper) {
return range(lower, BoundType.OPEN, upper, BoundType.OPEN);
}
public static IntRange open(int lower, int upper, UnaryOperator<Integer> func) {
return range(lower, BoundType.OPEN, upper, BoundType.OPEN, func);
}
public static IntRange open(int upper) {
return range(0, BoundType.CLOSED, upper, BoundType.OPEN);
}
public static IntRange open(int upper, UnaryOperator<Integer> func) {
return range(0, BoundType.CLOSED, upper, BoundType.OPEN, func);
}
public static IntRange openClosed(int lower, int upper) {
return range(lower, BoundType.OPEN, upper, BoundType.CLOSED);
}
public static IntRange openClosed(int lower, int upper, UnaryOperator<Integer> func) {
return range(lower, BoundType.OPEN, upper, BoundType.CLOSED, func);
}
public static IntRange closedOpen(int lower, int upper) {
return range(lower, BoundType.CLOSED, upper, BoundType.OPEN);
}
public static IntRange closedOpen(int lower, int upper, UnaryOperator<Integer> func) {
return range(lower, BoundType.CLOSED, upper, BoundType.OPEN, func);
}
public static IntRange closed(int lower, int upper) {
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED);
}
public static IntRange closed(int lower, int upper, UnaryOperator<Integer> func) {
return range(lower, BoundType.CLOSED, upper, BoundType.CLOSED, func);
}
public static IntRange closed(int upper) {
return range(0, BoundType.CLOSED, upper, BoundType.CLOSED);
}
public static IntRange closed(int upper, UnaryOperator<Integer> func) {
return range(0, BoundType.CLOSED, upper, BoundType.CLOSED, func);
}
public static IntRange singleton(int value) {
return range(value, BoundType.CLOSED, value, BoundType.CLOSED);
}
public static IntRange singleton(int value, UnaryOperator<Integer> func) {
return range(value, BoundType.CLOSED, value, BoundType.CLOSED, func);
}
private class FastIter implements Iterator<Integer> {
int now;
public FastIter() {
now = lower;
}
@Override
public final boolean hasNext() {
return now <= upper;
}
@Override
public final Integer next() {
return now++;
}
@Override
public final void remove() {
throw new UnsupportedOperationException();
}
}
private class Iter implements Iterator<Integer> {
int now;
public Iter() {
now = lower;
}
@Override
public final boolean hasNext() {
return now <= upper;
}
@Override
public final Integer next() {
int ret = now;
now = func.apply(now);
return ret;
}
@Override
public final void remove() {
throw new UnsupportedOperationException();
}
}
@Override
public Iterator<Integer> iterator() {
return lower == null || upper == null ? new EmptyIter() : useFastIter ? new FastIter() : new Iter();
}
@Override
public int getDistance() {
int ret = upper - lower;
if (upperType == BoundType.CLOSED) ++ ret;
return ret;
}
public int getClosedLower() {
return lower;
}
public int getOpenLower() {
return lower - 1;
}
public int getClosedUpper() {
return upperType == BoundType.CLOSED ? upper : upper - 1;
}
public int getOpenUpper() {
return upperType == BoundType.CLOSED ? upper + 1 : upper;
}
}
public interface Ring<T> {
public T add(T left, T right);
public T addUnit();
public T addInverse(T element);
public T multiply(T left, T right);
public T multiplyUnit();
public T multiplyInverse(T element);
}
public class ModInteger extends Number implements Ring<ModInteger>{
private static final long serialVersionUID = -8595710127161317579L;
private final int mod;
private int num;
public ModInteger(int mod) {
this.mod = mod;
num = 0;
}
public ModInteger(int mod, int num) {
this.mod = mod;
this.num = validNum(num);
}
public ModInteger(ModInteger n) {
mod = n.mod;
num = n.num;
}
private ModInteger(ModInteger n, int num) {
mod = n.mod;
this.num = num;
}
private int validNum(int n) {
n %= mod;
if (n < 0) n += mod;
return n;
}
protected int inverse(int n) {
int m = mod, u = 0, v = 1, t;
while(n != 0) {
t = m / n;
m -= t * n;
u -= t * v;
if (m != 0) {
t = n / m;
n -= t * m;
v -= t * u;
} else {
v %= mod;
if (v < 0) v += mod;
return v;
}
}
u %= mod;
if (u < 0) u += mod;
return u;
}
public boolean isPrime(int n) {
if ((n & 1) == 0) return false; // 偶数
for (int i = 3, j = 8, k = 9;k <= n;i += 2, k += j += 8) if (n % i == 0) return false;
return true;
}
@Override
public int intValue() {
return num;
}
@Override
public long longValue() {
return num;
}
@Override
public float floatValue() {
return num;
}
@Override
public double doubleValue() {
return num;
}
public ModInteger add(int n) {
return new ModInteger(this).addEqual(n);
}
public ModInteger add(ModInteger n) {
return new ModInteger(this).addEqual(n);
}
public ModInteger addEqual(int n) {
num = validNum(num + n);
return this;
}
public ModInteger addEqual(ModInteger n) {
if ((num += n.num) >= mod) num -= mod;
return this;
}
public ModInteger subtract(int n) {
return new ModInteger(this).subtractEqual(n);
}
public ModInteger subtract(ModInteger n) {
return new ModInteger(this).subtractEqual(n);
}
public ModInteger subtractEqual(int n) {
num = validNum(num - n);
return this;
}
public ModInteger subtractEqual(ModInteger n) {
if ((num -= n.num) < 0) num += mod;
return this;
}
@Override
public ModInteger add(ModInteger left, ModInteger right) {
return new ModInteger(left).addEqual(right);
}
@Override
public ModInteger addUnit() {
return new ModInteger(mod, 0);
}
@Override
public ModInteger addInverse(ModInteger element) {
return new ModInteger(element, element.mod - element.num);
}
public ModInteger multiply(int n) {
return new ModInteger(this).multiplyEqual(n);
}
public ModInteger multiply(ModInteger n) {
return new ModInteger(this).multiplyEqual(n);
}
public ModInteger multiplyEqual(int n) {
num = (int)((long)num * n % mod);
if (num < 0) num += mod;
return this;
}
public ModInteger multiplyEqual(ModInteger n) {
num = (int)((long)num * n.num % mod);
return this;
}
public ModInteger divide(int n) {
return new ModInteger(this).divideEqual(n);
}
public ModInteger divide(ModInteger n) {
return new ModInteger(this).divideEqual(n);
}
public ModInteger divideEqual(int n) {
num = (int)((long)num * inverse(validNum(n)) % mod);
return this;
}
public ModInteger divideEqual(ModInteger n) {
num = (int)((long)num * n.inverse(n.num) % mod);
return this;
}
@Override
public ModInteger multiply(ModInteger left, ModInteger right) {
return new ModInteger(left).multiplyEqual(right);
}
@Override
public ModInteger multiplyUnit() {
return new ModInteger(this, 1);
}
@Override
public ModInteger multiplyInverse(ModInteger element) {
return new ModInteger(element, element.inverse(element.num));
}
public ModInteger pow(int n) {
return new ModInteger(this).powEqual(n);
}
public ModInteger pow(ModInteger n) {
return new ModInteger(this).powEqual(n);
}
public ModInteger powEqual(int n) {
long ans = 1, num = this.num;
if (n < 0) {
n = -n;
while (n != 0) {
if ((n & 1) != 0) ans = ans * num % mod;
n >>>= 1;
num = num * num % mod;
}
this.num = inverse((int)ans);
return this;
}
while (n != 0) {
if ((n & 1) != 0) ans = ans * num % mod;
n >>>= 1;
num = num * num % mod;
}
this.num = (int)ans;
return this;
}
public ModInteger powEqual(ModInteger n) {
long num = this.num;
this.num = 1;
int mul = n.num;
while (mul != 0) {
if ((mul & 1) != 0) this.num *= num;
mul >>>= 1;
num *= num;
num %= mod;
}
return this;
}
public ModInteger equal(int n) {
num = validNum(n);
return this;
}
public ModInteger equal(ModInteger n) {
num = n.num;
return this;
}
public int toInt() {
return num;
}
public int getMod() {
return mod;
}
@Override
public boolean equals(Object x) {
if (x instanceof ModInteger) return ((ModInteger)x).num == num && ((ModInteger)x).mod == mod;
return false;
}
@Override
public int hashCode() {
return num ^ mod;
}
@Override
public String toString() {
return String.valueOf(num);
}
@Deprecated
public String debug() {
int min = num, ans = 1;
for (int i = 2;i < min;++ i) {
int tmp = multiply(i).num;
if (min > tmp) {
min = tmp;
ans = i;
}
}
return min + "/" + ans;
}
}
/**
* 素数を法とする演算上で、組み合わせの計算を高速に行います。
* @author 31536000
*
*/
public class ModUtility {
private final int mod, totient;
private int[] fact, inv, invfact;
/**
* modを法とする
* @param mod
*/
public ModUtility(int mod) {
this(mod, 2);
}
public ModUtility(int mod, int calc) {
if (mod <= 0) throw new IllegalArgumentException("illegal mod: " + mod);
this.mod = mod;
int totient = mod;
for (int i = 2;i * i <= mod;++ i) {
if (mod % i == 0) {
totient = totient / i * (i - 1);
while ((mod %= i) % i == 0);
}
}
this.totient = totient;
precalc(calc);
}
public void precalc(int calc) {
if (calc < 2) calc = 2;
fact = new int[calc];
inv = new int[calc];
invfact = new int[calc];
fact[0] = invfact[0] = fact[1] = invfact[1] = inv[1] = 1;
for (int i = 2;i < calc;++ i) {
fact[i] = (int)((long)fact[i - 1] * i % mod);
inv[i] = (int)(mod - (long)inv[mod % i] * (mod / i) % mod);
invfact[i] = (int)((long)invfact[i - 1] * inv[i] % mod);
}
}
public ModInteger create() {
return create(0);
}
public ModInteger create(int n) {
return new ModInt(n);
}
private class ModInt extends ModInteger {
private static final long serialVersionUID = -2435281861935422575L;
public ModInt(int n) {
super(mod, n);
}
@Override
protected int inverse(int n) {
return ModUtility.this.inverse(n);
}
}
public int inverse(int n) {
try {
if (inv.length > n) return inv[n];
int m = mod, u = 0, v = 1, t;
while(n != 0) {
t = m / n;
m -= t * n;
u -= t * v;
if (m != 0) {
t = n / m;
n -= t * m;
v -= t * u;
} else {
v %= mod;
if (v < 0) v += mod;
return v;
}
}
u %= mod;
if (u < 0) u += mod;
return u;
} catch (ArrayIndexOutOfBoundsException e) {
throw new IllegalArgumentException();
}
}
public int factorial(int n) {
try {
if (fact.length > n) return fact[n];
long ret = fact[fact.length - 1];
for (int i = fact.length;i <= n;++ i) ret = ret * i % mod;
return (int)ret;
} catch (ArrayIndexOutOfBoundsException e) {
throw new IllegalArgumentException();
}
}
public int permutation(int n, int k) {
if (k < 0) throw new IllegalArgumentException();
if (n < k) return 0;
if (fact.length > n) return (int)((long)fact[n] * invfact[n - k] % mod);
long ret = 1;
for (int i = n - k + 1;i <= n;++ i) ret = ret * i % mod;
return (int)ret;
}
public int combination(int n, int k) {
if (k < 0) throw new IllegalArgumentException();
if (n < k) return 0;
if (fact.length > n) return (int)((long)fact[n] * invfact[k] % mod * invfact[n - k] % mod);
long ret = 1;
if (n < 2 * k) k = n - k;
if (invfact.length > k) ret = invfact[k];
else ret = inverse(factorial(k));
for (int i = n - k + 1;i <= n;++ i) ret = ret * i % mod;
return (int)ret;
}
public int multinomial(int n, int... k) {
int sum = 0;
for (int i : k) sum += i;
long ret = factorial(n);
if (fact.length > n) {
for (int i : k) {
if (i < 0) throw new IllegalArgumentException();
ret = ret * invfact[i] % mod;
sum += i;
}
if (sum > n) return 0;
ret = ret * invfact[n - sum] % mod;
} else {
for (int i : k) {
if (i < 0) throw new IllegalArgumentException();
if (invfact.length > i) ret = ret * invfact[i] % mod;
else ret = ret * inverse(factorial(i)) % mod;
sum += i;
}
if (sum > n) return 0;
if (invfact.length > n - sum) ret = ret * invfact[n - sum] % mod;
else ret = ret * inverse(factorial(n - sum)) % mod;
}
return (int)ret;
}
public int multichoose(int n, int k) {
return combination(n + k - 1, k);
}
public int pow(int n, int m) {
long ans = 1, num = n;
if (m < 0) {
m = -m;
while (m != 0) {
if ((m & 1) != 0) ans = ans * num % mod;
m >>>= 1;
num = num * num % mod;
}
return inverse((int)ans);
}
while (m != 0) {
if ((m & 1) != 0) ans = ans * num % mod;
m >>>= 1;
num = num * num % mod;
}
return (int)ans;
}
public int totient() {
return totient;
}
public boolean isPrime() {
return totient == mod - 1;
}
public int mod(int n) {
return (n %= mod) < 0 ? n + mod : n;
}
public int add(int n, int m) {
return mod(n + m);
}
public int subtract(int n, int m) {
return mod(n - m);
}
public int multiply(int n, int m) {
int ans = (int)((long)n * m % mod);
return ans < 0 ? ans + mod : ans;
}
public int divide(int n, int m) {
return multiply(n, inverse(m));
}
}
}