Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {
	static void solve() {
		int n = ni(), k = ni();
		long[] a = nla(n);
		
		//debug
		Random ran = new Random();
		n = 100000; k = 5000;
		a = new long[n];
		for(int i=0;i<n;i++) {
			a[i] = ran.nextInt(1000000000);
			if(ran.nextInt() < 500000000) a[i] *= -1;
		}
		
		//絶対に0を選ぶしかないなら0
		int zero = 0;
		for(int i=0;i<n;i++) {
			if(a[i] == 0) zero ++ ;
		}
		if(k + zero > n) {
			out.println(0);
			return;
		}
		
		List<Long> p = new ArrayList<>();
		List<Long> m = new ArrayList<>();
		for(int i=0;i<n;i++) {
			if(a[i] > 0) p.add(a[i]);
			else if(a[i] < 0) m.add(a[i]);
		}
		Collections.sort(p, Comparator.reverseOrder());
		Collections.sort(m);
		int pn = p.size(), mn = m.size();
		long pCum[] = new long[pn + 1]; 
		long mCum[] = new long[mn + 1]; 
		pCum[0] = mCum[0] = 1;
		//cntでmodで割った回数を数える
		//正について
		long[] pModCnt = new long[pn+1]; //0が正, 1が負
		for(int i=0;i<pn;i++) {
			pCum[i+1] = pCum[i] * p.get(i);
			pModCnt[i+1] = pModCnt[i];
			if(pCum[i+1] >= mod) {
				pModCnt[i+1] += pCum[i+1] / mod;
				pCum[i+1] %= mod;
			}
		}
		//負についても
		long [] mModCnt = new long[mn+1]; //0が正, 1が負
		for(int i=0;i<mn;i++) {
			mCum[i+1] = mCum[i] * Math.abs(m.get(i));//絶対値に直して
			mModCnt[i+1] = mModCnt[i];
			if(mCum[i+1] >= mod) {
				mModCnt[i+1] += mCum[i+1] / mod;
				mCum[i+1] %= mod;
			}
		}
		
		//負数を奇数回選ぶ場合
		if((pn + mn - k == 0 && mn % 2 == 1) || (pn == 0 && k % 2 == 1)) {
			//0があるなら0にする
			if(zero > 0) {
				out.println(0);
				return;
			}
			//なるべく小さくする
			PriorityQueue<Long> pq = new PriorityQueue<>();
			for(int i=0;i<n;i++) {
				pq.add(Math.abs(a[i]));
			}
			long ans = 1;
			for(int i=0;i<k;i++) {
				ans *= pq.poll();
				ans %= mod;
			}
			ans = sub(0, ans);
			out.println(ans);
			return;
		}
		
		//負数を偶数回選べる場合
		long maxModCnt = 0;
		long max = -linf;
		for(int i=0;i<=min(mn, k);i+=2) {
			int pNum = k - i;
			if(pNum > pn)continue;
			long modCnt = pModCnt[pNum] + mModCnt[i];
			long t = pCum[pNum] * mCum[i];
			if(t >= mod) {
				modCnt += t / mod;
				t %= mod;
			}
			if(modCnt > maxModCnt) {
				max = t;
				maxModCnt = modCnt;
			}
			else if(modCnt == maxModCnt) {
				if(t > max) {
					max = t;
				}
			}
		}
		
		out.println(max);
		
	}
	
	//constant
	static final int inf = Integer.MAX_VALUE / 2;
	static final long linf = Long.MAX_VALUE / 3;
	static final double dinf = Double.MAX_VALUE / 3;
	static final long mod = (long) 1e9 + 7;
	static final int[] dx = { -1, 0, 1, 0 }, dy = { 0, -1, 0, 1 }, dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final double eps = 1e-10, pi = Math.PI;
	static StringBuilder sb = new StringBuilder();
	
	//libraries
	static void reverse(int ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(long ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(double ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void reverse(char ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static String getReverse(String s) {
		char c[] = s.toCharArray();
		reverse(c);
		s = String.valueOf(c);
		return s;
	}
	static <T> void reverse(List<T> ls) {
		int sz = ls.size();
		for (int i = 0; i < sz / 2; i++) {
			T t = ls.get(i);
			ls.set(i, ls.get(sz - 1 - i));
			ls.set(sz - 1 - i, t);
		}
	}
	static <T> void reverse(T[] ar) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			T t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}
	static void sbnl() {//StringBuilderに改行文字をappendする
		sb.append("\n");
	}
	static int lowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int upperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rlowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rupperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int lowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int upperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rlowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rupperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int lowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int upperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rlowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rupperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int lowerBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int upperBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rlowerBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static int rupperBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}
	static <T> int lowerBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) >= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}
	static <T> int upperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) > 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}
	static <T> int rupperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) < 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}
	static <T> int rlowerBound(List<T> ls, T x) {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) <= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}
	static int[] concat(int x, int arr[]) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}
	static int[] concat(int arr[], int x) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static long[] concat(long x, long arr[]) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}
	static long[] concat(long arr[], long x) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static char[] concat(char x, char arr[]) {
		char ret[] = new char[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static char[] concat(char arr[], char x) {
		char ret[] = new char[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}
	static int max(int x, int y) {
		return Math.max(x, y);
	}
	static int min(int x, int y) {
		return Math.min(x, y);
	}
	static int max(int x, int y, int z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static int min(int x, int y, int z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static long max(long x, long y) {
		return Math.max(x, y);
	}
	static long min(long x, long y) {
		return Math.min(x, y);
	}
	static long max(long x, long y, long z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static long min(long x, long y, long z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static double max(double x, double y) {
		return Math.max(x, y);
	}
	static double min(double x, double y) {
		return Math.min(x, y);
	}
	static double max(double x, double y, double z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}
	static double min(double x, double y, double z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}
	static void sort(int[] ar) {
		Arrays.sort(ar);
	}
	static void sort(long[] ar) {
		Arrays.sort(ar);
	}
	static void sort(double[] ar) {
		Arrays.sort(ar);
	}
	static void sort(char[] ar) {
		Arrays.sort(ar);
	}
	static void rsort(int[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(long[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(double[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void rsort(char[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}
	static void fill(int arr[], int x) {
		Arrays.fill(arr, x);
	}
	static void fill(long arr[], long x) {
		Arrays.fill(arr, x);
	}
	static void fill(boolean arr[], boolean x) {
		Arrays.fill(arr, x);
	}
	static void fill(double arr[], double x) {
		Arrays.fill(arr, x);
	}
	static void fill(int arr[][], int x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(long arr[][], long x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(double arr[][], double x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	static void fill(boolean arr[][], boolean x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}
	//MOD culc
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}
	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}
	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}
	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}
	//input
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	private static 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 static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}
	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}
	@SuppressWarnings("unused")
	private static double nd() {
		return Double.parseDouble(ns());
	}
	@SuppressWarnings("unused")
	private static char nc() {
		return (char) skip();
	}
	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	private static 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);
	}
	@SuppressWarnings("unused")
	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}
	@SuppressWarnings("unused")
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	@SuppressWarnings("unused")
	private static long[] nla(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}
	
	@SuppressWarnings("unused")
	private static int[][] nas(int n, int m){
		int[][] res = new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				res[i][j] = ni();
			}
		}
		return res;
	}
	
	@SuppressWarnings("unused")
	private static long[][] nlas(int n, int m){
		long[][] res = new long[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				res[i][j] = nl();
			}
		}
		return res;
	}
	
	@SuppressWarnings("unused")
	private static 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();
		}
	}
	@SuppressWarnings("unused")
	private static 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();
		}
	}
}