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 11.0.6) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
import java.util.function.BinaryOperator;


public class Main {
    private final static long mod = 1000000007;

    private final static int MAXN = 1000001;

    private static long power(long x, long y, long m) {
        long temp;
        if (y == 0)
            return 1;
        temp = power(x, y / 2, m);
        temp = (temp * temp) % m;
        if (y % 2 == 0)
            return temp;
        else
            return ((x % m) * temp) % m;
    }

    private static long power(long x, long y) {
        return power(x, y, mod);
    }

    private static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static int nextPowerOf2(int a) {
        return 1 << nextLog2(a);
    }

    static int nextLog2(int a) {
        return (a == 0 ? 0 : 32 - Integer.numberOfLeadingZeros(a - 1));
    }

    private static long modInverse(long a, long m) {
        long m0 = m;
        long y = 0, x = 1;
        if (m == 1)
            return 0;
        while (a > 1) {
            long q = a / m;
            long t = m;
            m = a % m;
            a = t;
            t = y;
            y = x - q * y;
            x = t;
        }
        if (x < 0)
            x += m0;
        return x;
    }

    private static int[] getLogArr(int n) {
        int arr[] = new int[n + 1];
        for (int i = 1; i < n + 1; i++) {
            arr[i] = (int) (Math.log(i) / Math.log(2) + 1e-10);
        }
        return arr;
    }

    private static int log[] = getLogArr(MAXN);

    private static int getLRSpt(int st[][], int L, int R, BinaryOperator<Integer> binaryOperator) {
        int j = log[R - L + 1];
        return binaryOperator.apply(st[L][j], st[R - (1 << j) + 1][j]);
    }

    private static int[][] getSparseTable(int array[], BinaryOperator<Integer> binaryOperator) {
        int k = log[array.length + 1] + 1;
        int st[][] = new int[array.length + 1][k + 1];

        for (int i = 0; i < array.length; i++)
            st[i][0] = array[i];

        for (int j = 1; j <= k; j++) {
            for (int i = 0; i + (1 << j) <= array.length; i++) {
                st[i][j] = binaryOperator.apply(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
            }
        }
        return st;
    }

    static class Subset {
        int parent;
        int rank;

        @Override
        public String toString() {
            return "" + parent;
        }
    }

    static int find(Subset[] Subsets, int i) {
        if (Subsets[i].parent != i)
            Subsets[i].parent = find(Subsets, Subsets[i].parent);
        return Subsets[i].parent;
    }

    static void union(Subset[] Subsets, int x, int y) {
        int xroot = find(Subsets, x);
        int yroot = find(Subsets, y);

        if (Subsets[xroot].rank < Subsets[yroot].rank)
            Subsets[xroot].parent = yroot;
        else if (Subsets[yroot].rank < Subsets[xroot].rank)
            Subsets[yroot].parent = xroot;
        else {
            Subsets[xroot].parent = yroot;
            Subsets[yroot].rank++;
        }
    }


    private static int maxx(Integer... a) {
        return Collections.max(Arrays.asList(a));
    }

    private static int minn(Integer... a) {
        return Collections.min(Arrays.asList(a));
    }


    private static long maxx(Long... a) {
        return Collections.max(Arrays.asList(a));
    }

    private static long minn(Long... a) {
        return Collections.min(Arrays.asList(a));
    }

    private static class Pair<T, U> implements Comparable<Pair<T, U>> {
        T a;
        U b;

        public Pair(T a, U b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return a.equals(pair.a) &&
                    b.equals(pair.b);
        }

        @Override
        public int hashCode() {
            return Objects.hash(a, b);
        }

        @Override
        public String toString() {
            return "(" + a +
                    "," + b +
                    ')';
        }

        @Override
        public int compareTo(Pair<T, U> o) {
            return (int) (this.a.equals(o.a) ?
                    this.b.equals(o.b) ? 0 :
                            ((Integer) this.b - (Integer) o.b) / Math.abs((Integer) this.b - (Integer) o.b) :
                    ((Integer) this.a - (Integer) o.a) / Math.abs((Integer) this.a - (Integer) o.a));
        }
    }


    public static int upperBound(List<Integer> list, int value) {
        int low = 0;
        int high = list.size();
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value >= list.get(mid)) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }


    private static int[] getLPSArray(String pattern) {
        int i, j, n = pattern.length();
        int[] lps = new int[pattern.length()];
        lps[0] = 0;
        for (i = 1, j = 0; i < n; ) {
            if (pattern.charAt(i) == pattern.charAt(j)) {
                lps[i++] = ++j;
            } else if (j > 0) {
                j = lps[j - 1];
            } else {
                lps[i++] = 0;
            }
        }
        return lps;
    }

    private static List<Integer> findPattern(String text, String pattern) {
        List<Integer> matchedIndexes = new ArrayList<>();
        if (pattern.length() == 0) {
            return matchedIndexes;
        }
        int[] lps = getLPSArray(pattern);
        int i = 0, j = 0, n = text.length(), m = pattern.length();
        while (i < n) {
            if (text.charAt(i) == pattern.charAt(j)) {
                i++;
                j++;
            }
            if (j == m) {
                matchedIndexes.add(i - j);
                j = lps[j - 1];
            }
            if (i < n && text.charAt(i) != pattern.charAt(j)) {
                if (j > 0) {
                    j = lps[j - 1];
                } else {
                    i++;
                }
            }
        }
        return matchedIndexes;
    }

    private static Set<Long> getDivisors(long n) {
        Set<Long> divisors = new HashSet<>();
        divisors.add(1L);
        divisors.add(n);
        for (long i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                divisors.add(i);
                divisors.add(n / i);
            }
        }
        return divisors;
    }

    private static long getLCM(long a, long b) {
        return (Math.max(a, b) / gcd(a, b)) * Math.min(a, b);
    }

    static long fac[] = new long[2000005];
    static long ifac[] = new long[2000005];

    private static void preCompute(int n) {
        fac = new long[n + 1];
        ifac = new long[n + 1];
        fac[0] = ifac[0] = fac[1] = ifac[1] = 1;
        int i;
        for (i = 2; i < n + 1; i++) {
            fac[i] = (i * fac[i - 1]) % mod;
            ifac[i] = (power(i, mod - 2) * ifac[i - 1]) % mod;
        }
    }

    private static long C(int n, int r) {
        if (n < 0 || r < 0) return 1;
        if (r > n) return 1;
        return (fac[n] * ((ifac[r] * ifac[n - r]) % mod)) % mod;
    }



    static long getSum(long BITree[], int index)
    {
        long sum = 0;
        index = index + 1;
        while(index>0)
        {
            index -= index & (-index);
        }
        return sum;
    }

    public static void updateBIT(long BITree[], int index, long val)
    {
        index = index + 1;
        while(index <= BITree.length-1) {
            BITree[index] += val;
            index += index & (-index);
        }
    }
    long[] constructBITree(int arr[], int m)
    {
        int n=arr.length;
        long BITree[] = new long[m+1];
        for(int i=1; i<=n; i++)
            BITree[i] = 0;
        for(int i = 0; i < n; i++)
            updateBIT(BITree, i, arr[i]);
        return BITree;
    }


    private static int upperBound(int a[], int l, int r, int x) {
        if(l>r)return -1;
        if(l==r){
            if(a[l]<=x) {
                return -1;
            }
            else{
                return a[l];
            }
        }
        int m=(l+r)/2;
        if(a[m]<=x) {
            return upperBound(a, m+1,r,x);
        }
        else {
            return upperBound(a, l,m,x);
        }
    }




    private static void mul(long A[][], long B[][]){
        int i,j,k,n=A.length;
        long C[][]=new long[n][n];
        for(i=0;i<n;i++){
            for(j=0;j<n;j++){
                for(k=0;k<n;k++){
                    C[i][j]=(C[i][j]+(A[i][k]*B[k][j])%mod)%mod;
                }
            }
        }
        for(i=0;i<n;i++) {
            for (j = 0; j < n; j++) {
                A[i][j]=C[i][j];
            }
        }
    }

    private static void power(long A[][], long base[][], long n) {
        if(n<2){
            return;
        }
        power(A, base, n/2);
        mul(A,A);
        if(n%2==1){
            mul(A, base);
        }
    }

    private static int cntFacPow(long n, long k){
        if(k<2)return 0;
        int cnt=0;
        while (n%k==0){
            cnt++;
            n/=k;
        }
        return cnt;
    }


    private static void print(int ... a){
        System.out.println(Arrays.toString(a));
    }

    private static int[] get3(int a[], int i, int si){
        int ret[]=new int[3];
        ret[2]=Integer.MIN_VALUE;
        for(int j=i,k=0;j<a.length&&k<3;j++){
            if(si==j) continue;
            ret[k++]=a[j];
        }
        return ret;
    }

    static void reverse(int a[], int l, int r){
        while (l<r){
            int t=a[l];
            a[l]=a[r];
            a[r]=t;
            l++;
            r--;
        }
    }


    private static boolean isSorted(int a[]) {
        for(int i=0;i<a.length-1;i++){
            if(a[i]>a[i+1]) return false;
        }
        return true;
    }

    private static int mex(int a[]) {
        Set<Integer> set = new HashSet<>();
        for(int i=0;i<a.length;i++){
            set.add(a[i]);
        }
        for(int i=0;i<a.length;i++){
            if(!set.contains(i))return i;
        }
        return a.length;
    }

    private static int findIdx(int a[], int x) {
        for(int i=0;i<a.length;i++) {
            if(a[i]==x)return i;
        }
        return -1;
    }

    private static int cntBlackMask(String grid[], int rowMask, int colMask) {
        int cnt=0;
        for(int i=0;i<grid.length;i++){
            for(int j=0;j<grid[i].length();j++){
                if(grid[i].charAt(j)=='#'&&(rowMask&(1<<i))==0&&(colMask&(1<<j))==0){
                    cnt++;
                }
            }
        }
        return cnt;
    }

    public static void main(String[] args) throws Exception {

        long START_TIME = System.currentTimeMillis();


        try (FastReader in = new FastReader();
             FastWriter out = new FastWriter()) {
            int n,t, i, j,f, k,m, ti, tidx, gm, q, g,h,w;
            //for (t = in.nextInt(), tidx = 1; tidx <= t; tidx++)
            {
                long x, y = 0, z = 0, sum = 0, bhc = 0, ans = 1,l,r;
                //out.print(String.format("Case #%d: ", tidx));
                n=in.nextInt();
                k=in.nextInt();
                Integer a[]=in.nextIntegerArr(n);
                int neg=0;
                Arrays.sort(a, Comparator.comparingInt(Math::abs));
                int lastneg=0;
                int lastpos=0;
                for(i=n-1,j=0;i>=0&&j<k;i--,j++){
                    if(a[i]<0){
                        neg++;
                        lastneg=a[i];
                    }
                    else{
                        lastpos=a[i];
                    }
                    ans=(ans*a[i])%mod;
                }
                int nextpos=0,nextneg=0;
                if(neg%2==1){
                    for(;i>=0;i--){
                        if(a[i]<0&&nextneg==0){
                            nextneg=a[i];
                        }
                        if(a[i]>0&&nextpos==0){
                            nextpos=a[i];
                        }
                    }
                    double r1=0,r2=0,r3=0,r4=0;
                    if(lastpos!=0&&nextneg!=0){
                        r1=1.0*nextneg/lastpos;
                    }
                    if(lastneg!=0&&nextpos!=0){
                        r2=1.0*nextpos/lastneg;
                    }
                    if(Math.abs(r1)>Math.abs(r2)&&r2>1e-9){
                        ans=(((ans*power(lastpos, mod - 2))%mod)*nextneg)%mod;
                    }
                    else if(r2>1e-9){
                        ans=(((ans*power(lastneg, mod - 2))%mod)*nextpos)%mod;
                    }
                    else{
                        ans=1;
                        for(j=0;j<k;j++){
                            ans=(ans*a[j])%mod;
                        }
                    }
                }
                ans=(ans%mod+mod)%mod;
                out.println(ans);
            }
            if (args.length > 0 && "ex_time".equals(args[0])) {
                out.print("\nTime taken: ");
                out.println(System.currentTimeMillis() - START_TIME);
            }
            out.commit();
        } catch (Exception e) {
            e.printStackTrace();
        }


    }




    public static class FastReader implements Closeable {
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st;

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] nextIntArr(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        Integer[] nextIntegerArr(int n) {
            Integer[] arr = new Integer[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        double[] nextDoubleArr(int n) {
            double[] arr = new double[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextDouble();
            }
            return arr;
        }

        long[] nextLongArr(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        String[] nextStrArr(int n) {
            String[] arr = new String[n];
            for (int i = 0; i < n; i++) {
                arr[i] = next();
            }
            return arr;
        }


        int[][] nextIntArr2(int n, int m) {
            int[][] arr = new int[n][m];
            for (int i = 0; i < n; i++) {
                arr[i] = nextIntArr(m);
            }
            return arr;
        }

        long[][] nextLongArr2(int n, int m) {
            long[][] arr = new long[n][m];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLongArr(m);
            }
            return arr;
        }

        @Override
        public void close() throws IOException {
            br.close();
        }
    }


    public static class FastWriter implements Closeable {
        BufferedWriter bw;
        StringBuilder sb = new StringBuilder();
        List<String> list = new ArrayList<>();
        Set<String> set = new HashSet<>();

        public FastWriter() {
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        <T> void commit() throws IOException {
            bw.write(sb.toString());
            bw.flush();
            sb = new StringBuilder();
        }

        public <T> void print(T obj) throws IOException {
            sb.append(obj.toString());
        }

        public void println() throws IOException {
            print("\n");
        }

        public <T> void println(T obj) throws IOException {
            print(obj.toString() + "\n");
        }

        <T> void printArrLn(T[] arr) throws IOException {
            for (int i = 0; i < arr.length - 1; i++) {
                print(arr[i] + " ");
            }
            println(arr[arr.length - 1]);
        }

        <T> void printArr2(T[][] arr) throws IOException {
            for (int j = 0; j < arr.length; j++) {
                for (int i = 0; i < arr[j].length - 1; i++) {
                    print(arr[j][i] + " ");
                }
                println(arr[j][arr[j].length - 1]);
            }
        }

        <T> void printColl(Collection<T> coll) throws IOException {
            for (T e : coll) {
                print(e + " ");
            }
            println();
        }

        void printCharN(char c, int n) throws IOException {
            for (int i = 0; i < n; i++) {
                print(c);
            }
        }

        void printIntArr2(int[][] arr) throws IOException {
            for (int j = 0; j < arr.length; j++) {
                for (int i = 0; i < arr[j].length - 1; i++) {
                    print(arr[j][i] + " ");
                }
                println(arr[j][arr[j].length - 1]);
            }
        }

        @Override
        public void close() throws IOException {
            bw.close();
        }

    }

}