Problem: There are N oases on a number line. The coordinate of the i-th oases from the left is x_i.

Camel hopes to visit all these oases. Initially, the volume of the hump on his back is V. When the volume of the hump is v, water of volume at most v can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times.

Camel can travel on the line by either walking or jumping:

* Walking over a distance of d costs water of volume d from the hump. A walk that leads to a negative amount of stored water cannot be done.
* Let v be the amount of water stored at the moment. When v>0, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes v/2 (rounded down to the nearest integer), and the amount of stored water becomes 0.



For each of the oases, determine whether it is possible to start from that oasis and visit all the oases.

Constraints

* 2 ≤ N,V ≤ 2 × 10^5
* -10^9 ≤ x_1 < x_2 < ... < x_N ≤ 10^9
* V and x_i are all integers.

Input

Input is given from Standard Input in the following format:


N V
x_1 x_2 ... x_{N}


Output

Print N lines. The i-th line should contain `Possible` if it is possible to start from the i-th oasis and visit all the oases, and `Impossible` otherwise.

Examples

Input

3 2
1 3 6


Output

Possible
Possible
Possible


Input

7 2
-10 -4 -2 0 2 4 10


Output

Impossible
Possible
Possible
Possible
Possible
Possible
Impossible


Input

16 19
-49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84


Output

Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Possible
Impossible
Impossible
Impossible
Impossible

Solution (in JAVA):

Solution:
// package atcoder.agc.agc012;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int v = in.nextInt();

        int[] x = in.nextInts(n);
        int vv = v;
        int maxJump = 0;
        while (vv >= 1) {
            maxJump++;
            vv /= 2;
        }
        maxJump++;

        int[][] nextRight = new int[maxJump][n];
        for (int d = 0 ; d < maxJump ; d++) {
            int canGo = v >>> d;

            for (int i = 0 ; i < n ;) {
                int j = i+1;
                while (j < n && x[j] - x[j-1] <= canGo) {
                    j++;
                }
                for (int k = i ; k < j ; k++) {
                    nextRight[d][k] = j;
                }
                i = j;
            }
        }

        int requiredStep = 0;
        for (int i = 0 ; i < n ; ) {
            int j = nextRight[0][i];
            requiredStep++;
            i = j;
        }
        if (requiredStep >= 22) {
            for (int i = 0; i < n ; i++) {
                out.println("Impossible");
            }
            out.flush();
            return;
        }

        int[][] nextLeft = new int[maxJump][n];
        for (int d = 0 ; d < maxJump ; d++) {
            int canGo = v >>> d;
            for (int i = n-1 ; i >= 0 ;) {
                int j = i-1;
                while (j >= 0 && x[j+1] - x[j] <= canGo) {
                    j--;
                }
                for (int k = i ; k > j ; k--) {
                    nextLeft[d][k] = j;
                }
                i = j;
            }
        }

        int[] dpLeft = new int[1<<maxJump];
        for (int i = 0 ; i < (1<<maxJump) ; i += 2) {
            for (int k = 1 ; k < maxJump ; k++) {
                if (((i >> k) & 1) == 0) {
                    int ti = i | (1<<k);
                    dpLeft[ti] = Math.max(dpLeft[ti], dpLeft[i] == n ? n : nextRight[k][dpLeft[i]]);

                }
            }
        }

        int[] dpRight = new int[1<<maxJump];
        Arrays.fill(dpRight, n-1);
        for (int i = 0 ; i < (1<<maxJump) ; i += 2) {
            for (int k = 1 ; k < maxJump ; k++) {
                if (((i >> k) & 1) == 0) {
                    int ti = i | (1<<k);
                    dpRight[ti] = Math.min(dpRight[ti], dpRight[i] == -1 ? -1 : nextLeft[k][dpRight[i]]);
                }
            }
        }

        for (int i = 0 ; i < n ; ) {
            boolean isOK = false;
            int from = nextLeft[0][i] + 1;
            int to = nextRight[0][i] - 1;
            int fullPtn = (1<<maxJump)-2;
            for (int leftPtn = 0 ; leftPtn < (1<<maxJump) ; leftPtn += 2) {
                int rightPtn = fullPtn-leftPtn;
                int leftPart = dpLeft[leftPtn];
                int rightPart = dpRight[rightPtn];
                if (from <= leftPart && rightPart <= to) {
                    isOK = true;
                    break;
                }
            }
            for (int j = from ; j <= to ; j++) {
                out.println(isOK ? "Possible" : "Impossible");
            }
            i = to+1;
        }
        out.flush();
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int[] nextInts(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }


        private int[][] nextIntTable(int n, int m) {
            int[][] ret = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextInt();
                }
            }
            return ret;
        }

        private long[] nextLongs(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextLong();
            }
            return ret;
        }

        private long[][] nextLongTable(int n, int m) {
            long[][] ret = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextLong();
                }
            }
            return ret;
        }

        private double[] nextDoubles(int n) {
            double[] ret = new double[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextDouble();
            }
            return ret;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}