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: Accepted)

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

public class Main {

    public static void main(String args[]) throws IOException {
        InOut inout = new InOut();
        Resolver resolver = new Resolver(inout);
        resolver.solve();
        inout.flush();
    }

    private static class Resolver {

        final long LONG_INF = (long) 1e18;
        final int INF = (int) (1e9 + 7);
        final int MOD = 998244353;
        long f[];
        InOut inout;

        Resolver(InOut inout) {
            this.inout = inout;
        }

        void initF(int n) {
            f = new long[n + 1];
            f[1] = 1;
            for (int i = 2; i <= n; i++) {
                f[i] = (f[i - 1] * i) % MOD;
            }
        }

        int d[] = {0, -1, 0, 1, 0};

        boolean legal(int r, int c, int n, int m) {
            return r >= 0 && r < n && c >= 0 && c < m;
        }

        void solve() throws IOException {
            int tt = 1;
            boolean hvt = false;
            if (hvt) {
                tt = nextInt();
            }
            for (int cs = 1; cs <= tt; cs++) {
                long rs = 0;
                int n = nextInt();
                int K = nextInt();
                long a[] = new long[n];
                long b[] = new long[n];
                int i = 0;
                int j = 0;
                for (int k = 0; k < n; k++) {
                    int c = nextInt();
                    if (c < 0) {
                        a[i++] = c;
                    } else if (c > 0) {
                        b[j++] = c;
                    }
                }
                Arrays.sort(a, 0, i);
                Arrays.sort(b, 0, j);
                for (int k = 0; k < i / 2; k++) {
                    swap(a, k, i - k - 1);
                }
                if (i + j >= K) {
                    rs = 1;
                    if (K == n) {
                        for (int k = 0; k < i; k++) {
                            rs = rs * a[k] % INF;
                        }
                        for (int k = 0; k < j; k++) {
                            rs = rs * b[k] % INF;
                        }
                    } else if (i == n && K % 2 == 1) {
                        for (int k = 0; k < K; k++) {
                            rs = (rs * a[k]) % INF;
                        }
                    } else if (i + j == K && i % 2 == 1 || j == 0 && K % 2 == 1) {
                        rs = 0;
                    } else {
                        if (K % 2 == 1 && j > 0) {
                            rs = b[--j];
                            K--;
                        }
                        while (i > 1 && j > 1 && K > 0) {
                            long f = a[i - 1] * a[i - 2];
                            long t = b[j - 1] * b[j - 2];
                            if (f > t) {
                                i -= 2;
                                rs = rs * (f % INF) % INF;
                            } else {
                                j -= 2;
                                rs = rs * (t % INF) % INF;
                            }
                            K -= 2;
                        }
                        while (i > 1 && K > 0) {
                            long f = a[i - 1] * a[i - 2] % INF;
                            i -= 2;
                            rs = rs * f % INF;
                            K -= 2;
                        }
                        while (j > 1 && K > 0) {
                            long t = b[j - 1] * b[j - 2] % INF;
                            j -= 2;
                            rs = rs * t % INF;
                            K -= 2;
                        }
                        if (K > 0) {
                            if (i > 0) {
                                rs = rs * a[0] % INF;
                            }
                            if (j > 0) {
                                rs = rs * b[0] % INF;
                            }
                        }
                    }
                }
                rs = (rs + INF) % INF;

                format("%d", rs);

                if (cs < tt) {
                    format("\n");
                }
//                flush();
            }
        }

        String next(int n) throws IOException {
            return inout.next(n);
        }

        String nextLine() throws IOException {
            return inout.nextLine();
        }

        int nextInt() throws IOException {
            return inout.nextInt();
        }

        long nextLong(int n) throws IOException {
            return inout.nextLong(n);
        }

        long[] anLong(int i, int j, int len) throws IOException {
            long a[] = new long[j + 1];
            for (int k = i; k <= j; k++) {
                a[k] = nextLong(len);
            }
            return a;
        }

        void print(String s, boolean nextLine) {
            inout.print(s, nextLine);
        }

        void format(String format, Object... obj) {
            inout.format(format, obj);
        }

        void flush() {
            inout.flush();
        }

        void swap(long a[], int i, int j) {
            a[i] ^= a[j];
            a[j] ^= a[i];
            a[i] ^= a[j];
        }

        int getP(int x, int p[]) {
            if (p[x] == 0 || p[x] == x) {
                return x;
            }
            return p[x] = getP(p[x], p);
        }

        void union(int x, int y, int p[]) {
            if (x < y) {
                p[y] = x;
            } else {
                p[x] = y;
            }
        }

        boolean topSort() {
            int n = adj.length - 1;
            int d[] = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 0; j < adj[i].size(); j++) {
                    d[adj[i].get(j)[0]]++;
                }
            }
            List<Integer> list = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                if (d[i] == 0) {
                    list.add(i);
                }
            }
            for (int i = 0; i < list.size(); i++) {
                for (int j = 0; j < adj[list.get(i)].size(); j++) {
                    int t = adj[list.get(i)].get(j)[0];
                    d[t]--;
                    if (d[t] == 0) {
                        list.add(t);
                    }
                }
            }
            return list.size() == n;
        }

        class BinaryIndexedTree {

            int n = 1;
            long C[];

            BinaryIndexedTree(int sz) {
                while (n <= sz) {
                    n <<= 1;
                }
                C = new long[n];
            }

            int lowbit(int x) {
                return x & -x;
            }

            void add(int x, long val) {
                while (x < n) {
                    C[x] += val;
                    x += lowbit(x);
                }
            }

            long getSum(int x) {
                long res = 0;
                while (x > 0) {
                    res += C[x];
                    x -= lowbit(x);
                }
                return res;
            }

            int binSearch(long sum) {
                if (sum == 0) {
                    return 0;
                }
                int n = C.length;
                int mx = 1;
                while (mx < n) {
                    mx <<= 1;
                }
                int res = 0;
                for (int i = mx / 2; i >= 1; i >>= 1) {
                    if (C[res + i] < sum) {
                        sum -= C[res + i];
                        res += i;
                    }
                }
                return res + 1;
            }
        }

        //Binary tree
        class TreeNode {
            int val;
            int tier = -1;
            TreeNode parent;
            TreeNode left;
            TreeNode right;

            TreeNode(int val) {
                this.val = val;
            }
        }

        //binary tree dfs
        void tierTree(TreeNode root) {
            if (null == root) {
                return;
            }
            if (null != root.parent) {
                root.tier = root.parent.tier + 1;
            } else {
                root.tier = 0;
            }
            tierTree(root.left);
            tierTree(root.right);
        }

        //LCA start
        TreeNode[][] lca;
        TreeNode[] tree;

        void lcaDfsTree(TreeNode root) {
            if (null == root) {
                return;
            }
            tree[root.val] = root;
            TreeNode nxt = root.parent;
            int idx = 0;
            while (null != nxt) {
                lca[root.val][idx] = nxt;
                nxt = lca[nxt.val][idx];
                idx++;
            }
            lcaDfsTree(root.left);
            lcaDfsTree(root.right);
        }

        TreeNode lcaTree(TreeNode root, int n, TreeNode x, TreeNode y) throws IOException {
            if (null == root) {
                return null;
            }
            if (-1 == root.tier) {
                tree = new TreeNode[n + 1];
                tierTree(root);
            }
            if (null == lca) {
                lca = new TreeNode[n + 1][31];
                lcaDfsTree(root);
            }
            int z = Math.abs(x.tier - y.tier);
            int xx = x.tier > y.tier ? x.val : y.val;
            while (z > 0) {
                final int zz = z;
                int l = (int) binSearch(0, 31
                        , k -> zz < (1 << k));
                xx = lca[xx][l].val;
                z -= 1 << l;
            }
            int yy = y.val;
            if (x.tier <= y.tier) {
                yy = x.val;
            }
            while (xx != yy) {
                final int xxx = xx;
                final int yyy = yy;
                int l = (int) binSearch(0, 31
                        , k -> (1 << k) <= tree[xxx].tier && lca[xxx][(int) k] != lca[yyy][(int) k]);
                xx = lca[xx][l].val;
                yy = lca[yy][l].val;
            }
            return tree[xx];
        }
        //LCA end

        //graph
        List<int[]> adj[];

        void initGraph(int n, int m, boolean hasW, boolean directed) throws IOException {
            adj = new List[n + 1];
            for (int i = 1; i <= n; i++) {
                adj[i] = new ArrayList<>();
            }
            for (int i = 0; i < m; i++) {
                int f = nextInt();
                int t = nextInt();
                int w = hasW ? nextInt() : 0;
                adj[f].add(new int[]{t, w});
                if (!directed) {
                    adj[t].add(new int[]{f, w});
                }
            }
        }

        long binSearch(long l, long r, BinSearch sort) throws IOException {
            while (l < r) {
                long m = l + (r - l) / 2;
                if (sort.binSearchCmp(m)) {
                    l = m + 1;
                } else {
                    r = m;
                }
            }
            return l;
        }

        void getDiv(Map<Integer, Integer> map, int n) {
            int sqrt = (int) Math.sqrt(n);
            for (int i = sqrt; i >= 2; i--) {
                if (n % i == 0) {
                    getDiv(map, i);
                    getDiv(map, n / i);
                    return;
                }
            }
            map.put(n, map.getOrDefault(n, 0) + 1);
        }

        boolean[] generatePrime(int n) {
            boolean p[] = new boolean[n + 1];
            p[2] = true;

            for (int i = 3; i <= n; i += 2) {
                p[i] = true;
            }

            for (int i = 3; i <= Math.sqrt(n); i += 2) {
                if (!p[i]) {
                    continue;
                }
                for (int j = i * i; j <= n; j += i << 1) {
                    p[j] = false;
                }
            }
            return p;
        }

        boolean isPrime(long n) { //determines if n is a prime number
            int p[] = {2, 3, 5, 233, 331};
            int pn = p.length;
            long s = 0, t = n - 1;//n - 1 = 2^s * t
            while ((t & 1) == 0) {
                t >>= 1;
                ++s;
            }
            for (int i = 0; i < pn; ++i) {
                if (n == p[i]) {
                    return true;
                }
                long pt = pow(p[i], t, n);
                for (int j = 0; j < s; ++j) {
                    long cur = llMod(pt, pt, n);
                    if (cur == 1 && pt != 1 && pt != n - 1) {
                        return false;
                    }
                    pt = cur;
                }
                if (pt != 1) {
                    return false;
                }
            }
            return true;
        }

        long llMod(long a, long b, long mod) {
            return (a * b - (long) ((double) a / mod * b + 0.5) * mod + mod) % mod;
//        long r = 0;
//        a %= mod;
//        b %= mod;
//        while (b > 0) {
//            if ((b & 1) == 1) {
//                r = (r + a) % mod;
//            }
//            b >>= 1;
//            a = (a << 1) % mod;
//        }
//        return r;
        }

        long pow(long a, long n) {
            long ans = 1;
            while (n > 0) {
                if ((n & 1) == 1) {
                    ans = ans * a;
                }
                a = a * a;
                n >>= 1;
            }
            return ans;
        }

        long pow(long a, long n, long mod) {
            long ans = 1;
            while (n > 0) {
                if ((n & 1) == 1) {
                    ans = llMod(ans, a, mod);
                }
                a = llMod(a, a, mod);
                n >>= 1;
            }
            return ans;
        }

        private long[][] initC(int n) {
            long c[][] = new long[n][n];

            for (int i = 0; i < n; i++) {
                c[i][0] = 1;
            }

            for (int i = 1; i < n; i++) {
                for (int j = 1; j <= i; j++) {
                    c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
                }
            }
            return c;
        }

        /**
         * ps: n >= m, choose m from n;
         */
        private int cmn(long n, long m) {
            if (m > n) {
                n ^= m;
                m ^= n;
                n ^= m;
            }
            m = Math.min(m, n - m);

            long top = 1;
            long bot = 1;
            for (long i = n - m + 1; i <= n; i++) {
                top = (top * i) % MOD;
            }
            for (int i = 1; i <= m; i++) {
                bot = (bot * i) % MOD;
            }

            return (int) ((top * pow(bot, MOD - 2, MOD)) % MOD);
        }

        long gcd(long a, long b) {
            if (a < b) {
                return gcd(b, a);
            }
            while (b != 0) {
                long tmp = a % b;
                a = b;
                b = tmp;
            }
            return a;
        }

        boolean isEven(long n) {
            return (n & 1) == 0;
        }

        interface BinSearch {
            boolean binSearchCmp(long k) throws IOException;
        }
    }

    private static class InOut {
        private BufferedReader br;
        private StreamTokenizer st;
        private PrintWriter pw;

        InOut() throws FileNotFoundException {
//            System.setIn(new FileInputStream("resources/inout/b1.in"));
//            System.setOut(new PrintStream("resources/inout/b1.out"));
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StreamTokenizer(br);
            pw = new PrintWriter(new OutputStreamWriter(System.out));
            st.ordinaryChar('\'');
            st.ordinaryChar('\"');
            st.ordinaryChar('/');
        }

        private long[] anLong(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        private String next(int len) throws IOException {
            char ch[] = new char[len];
            int cur = 0;
            char c;
            while ((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t') ;
            do {
                ch[cur++] = c;
            } while (!((c = (char) br.read()) == '\n' || c == '\r' || c == ' ' || c == '\t'));
            return String.valueOf(ch, 0, cur);
        }

        private int nextInt() throws IOException {
            st.nextToken();
            return (int) st.nval;
        }

        private long nextLong(int n) throws IOException {
            return Long.parseLong(next(n));
        }

        private double nextDouble() throws IOException {
            st.nextToken();
            return st.nval;
        }

        private String[] nextSS(String reg) throws IOException {
            return br.readLine().split(reg);
        }

        private String nextLine() throws IOException {
            return br.readLine();
        }

        private void print(String s, boolean newLine) {
            if (null != s) {
                pw.print(s);
            }
            if (newLine) {
                pw.println();
            }
        }

        private void format(String format, Object... obj) {
            pw.format(format, obj);
        }

        private void flush() {
            pw.flush();
        }
    }
}