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).

Examples

Input

4 2
1 2 -3 -4


Output

12


Input

4 3
-1 -2 -3 -4


Output

1000000001


Input

2 1
-1 1000000000


Output

1000000000


Input

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


Output

999983200

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;

public class Main implements Runnable { // クラス名はMain1

	PrintWriter out = new PrintWriter(System.out);
	InputReader sc = new InputReader(System.in);
	static int mod = (int) (1e9 + 7); //10^9+7
	int[] dx = { 1, 0, -1, 0 }, dy = { 0, 1, 0, -1 }; //4 directions

	public static void main(String[] args) {
		Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1));
		new Thread(null, new Main(), "", 1024 * 1024 * 1024).start(); // 16MBスタックを確保して実行
	}

	public void run() {

		try {
			//String S = sc.next().trim();
			int N = sc.nextInt();
			int K = sc.nextInt();
			long[] A = new long[N];
			ArrayList<Long> minus = new ArrayList<Long>();
			ArrayList<Long> plus = new ArrayList<Long>();
			for (int i = 0; i < N; i++) {
				long a = sc.nextLong();
				if (a < 0) {
					minus.add(a);
				} else {
					plus.add(a);
				}
				A[i] = a;
			}

			if (K == 1) {
				Collections.sort(plus, Collections.reverseOrder());
				Collections.sort(minus, Collections.reverseOrder());
				if (plus.size() > 0) {
					out.println(plus.get(0));
				} else {
					out.println(minus.get(0));
				}
				return;
			}

			if (K == N) {
				long ans = 1;
				for (int i = 0; i < N; i++) {
					ans = Math.multiplyExact(ans, A[i] % mod) % mod;
				}
				ans = ans % mod;
				if (ans < 0) {
					out.println(mod + ans % mod);
				} else {
					out.println(ans % mod);
				}
				return;
			}

			if (K % 2 == 0) {
				PriorityQueue<Long> pq = new PriorityQueue<>(Collections.reverseOrder());
				Collections.sort(minus);
				Collections.sort(plus, Collections.reverseOrder());
				for (int i = 0; i < minus.size(); i += 2) {
					long a = minus.get(i);
					if (i + 1 >= minus.size()) {
						break;
					}
					long b = minus.get(i + 1);
					long add = Math.multiplyExact(a, b);
					pq.add(add);
				}

				for (int i = 0; i < plus.size(); i += 2) {
					long a = plus.get(i);
					if (i + 1 >= plus.size()) {
						break;
					}
					long b = plus.get(i + 1);
					long add = Math.multiplyExact(a, b);
					pq.add(add);
				}
				int count = 0;
				long ans = 1;
				while (pq.size() > 0 && count < K / 2) {
					ans = Math.multiplyExact(ans, pq.poll() % mod) % mod;
					ans %= mod;
					count++;
				}
				ans %= mod;
				out.println(ans);
			} else {
				if (plus.size() >= 1) {
					PriorityQueue<Long> pq = new PriorityQueue<>(Collections.reverseOrder());
					Collections.sort(minus);
					Collections.sort(plus, Collections.reverseOrder());
					for (int i = 0; i < minus.size(); i += 2) {
						long a = minus.get(i);
						if (i + 1 >= minus.size()) {
							break;
						}
						long b = minus.get(i + 1);
						long add = Math.multiplyExact(a, b);
						pq.add(add);
					}

					for (int i = 1; i < plus.size(); i += 2) {
						long a = plus.get(i);
						if (i + 1 >= plus.size()) {
							break;
						}
						long b = plus.get(i + 1);
						long add = a * b;
						pq.add(add);
					}
					int count = 0;
					long ans = 1;
					while (pq.size() > 0 && count < K / 2) {
						ans = Math.multiplyExact(ans, pq.poll() % mod) % mod;
						count++;
					}
					ans = Math.multiplyExact(ans, plus.get(0) % mod) % mod;
					ans %= mod;
					out.println(ans);
				} else {
					Collections.sort(minus, Collections.reverseOrder());
					long ans = 1;
					for (int i = 0; i < K; i++) {
						ans = Math.multiplyExact(ans, Math.abs(minus.get(i)) % mod) % mod;
						//ans = Math.multiplyExact(ans, minus.get(i) % mod) % mod;
					}
					ans %= mod;
					out.println(mod - ans % mod);
				}
			}
			//out.println(Arrays.toString(A));

		} catch (ArithmeticException ae) {
			ae.printStackTrace();
			throw new RuntimeException();
		} catch (Exception e) {
			e.printStackTrace();
			throw new RuntimeException();
		} finally {
			out.flush();
			out.close();
		}

	}

	class InfoLong implements Comparable<InfoLong> {
		public int type;
		public long a;

		public InfoLong(int type, long a) {
			this.type = type;
			this.a = a;
		}

		@Override
		public int compareTo(InfoLong o) {
			if (this.type == o.type) {
				return Long.compare(o.a, this.a);
			} else {
				return Integer.compare(o.type, this.type);
			}
		}
	}

	class InfoInt implements Comparable<InfoInt> {
		public int a;
		public int b;

		public InfoInt(int a, int b) {
			this.a = a;
			this.b = b;
		}

		@Override
		public int compareTo(InfoInt o) {
			//return this.a - o.a;//昇順
			// return o.a - this.a;//降順
			//複数項目で並び替え。aの降順、aが同じならbの降順
			if (this.a == o.a) {
				return Integer.compare(o.b, this.b);
			} else {
				return Integer.compare(o.a, this.a);
			}
		}
	}

	//Arrays.sort(Sample,new Comp());
	class Comp implements Comparator<InfoLong> {
		public int compare(InfoLong be, InfoLong af) {
			return Long.compare(af.a, be.a);
		}
	}

	/**
	 *
	 * @param n
	 * @param m
	 * @return Combinationの数を返す(mod無しなので、大きい値には使用できない桁溢れする)
	 */
	long calcCombination(int n, int m) {
		if (n < m || m < 0) {
			throw new IllegalArgumentException("引数の値が不正です ( n : " + n + ", m : " + m + ")");
		}
		long c = 1;
		m = (n - m < m ? n - m : m);
		for (int ns = n - m + 1, ms = 1; ms <= m; ns++, ms++) {
			c *= ns;
			c /= ms;
		}
		return c;
	}

	/*
	 * 使用するときはModに注意。Global変数を参照
	 */
	public static long comb(long a, long b) {
		if (a < b)
			return 0;
		long res = 1;
		long inv = pow(fact(Math.min(b, a - b)), mod - 2);
		for (long i = a; i > a - Math.min(b, a - b); i--) {
			res *= i;
			res %= mod;
		}
		res *= inv;
		res %= mod;
		return res;
	}

	public static long pow(long x, long n) {
		long res = 1;
		while (n > 0) {
			if ((n & 1) == 1) {
				res *= x;
				res %= mod;
			}
			x *= x;
			x %= mod;
			n >>= 1;
		}
		return res;
	}

	public static long fact(long n) {
		long res = 1;
		while (n > 0) {
			res *= n;
			res %= mod;
			n--;
		}
		return res;
	}

	// 高速なScanner
	static class InputReader {
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

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

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}
