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 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 = new int[n];
        for (int i = 0; i < n ; i++) {
            x[i] = in.nextInt();
        }
        int[] revx = x.clone();
        for (int i = 0; i < x.length; i++) {
            revx[i] = -x[n-1-i];
        }

        int[] left = doit(V, x);
        int[] right = doit(V, revx);
        int[] top = stepV(V, x);

        UnionFind uf = new UnionFind(n);
        for (int i = 0; i < n ; ) {
            int j = i;
            while (j < n && top[i] == top[j]) {
                uf.unite(i, j);
                j++;
            }
            i = j;
        }

        boolean[] isOK = new boolean[n];
        int full = (1<<REDUCE)-1;
        for (int leftp = 0 ; leftp <= full ; leftp++) {
            if (left[leftp] + right[full-leftp] >= n) {
                Arrays.fill(isOK, true);
                continue;
            }

            int tc = top[left[leftp]];
            int rp = right[full-leftp];
            if (tc + rp >= n) {
                //debug(leftp, left[leftp], top[left[leftp]]);
                int id = uf.find(left[leftp]);
                isOK[id] = true;
                // ok!
            }
        }

        for (int i = 0; i < n ; i++) {
            out.println(isOK[uf.find(i)] ? "Possible" : "Impossible");
        }
        out.flush();
    }

    static int REDUCE = 19;

    static class UnionFind {
        int[] rank;
        int[] parent;
        int[] cnt;

        public UnionFind(int n) {
            rank = new int[n];
            parent = new int[n];
            cnt = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                cnt[i] = 1;
            }
        }

        public int find(int a) {
            if (parent[a] == a) {
                return a;
            }
            parent[a] = find(parent[a]);
            return parent[a];
        }

        public void unite(int a, int b) {
            a = find(a);
            b = find(b);
            if (a == b) {
                return;
            }
            if (rank[a] < rank[b]) {
                parent[a] = b;
                cnt[b] += cnt[a];
                cnt[a] = cnt[b];
            } else {
                parent[b] = a;
                cnt[a] += cnt[b];
                cnt[b] = cnt[a];
                if (rank[a] == rank[b]) {
                    rank[a]++;
                }
            }
        }

        public int groupCount(int a) {
            return cnt[find(a)];
        }

        private boolean issame(int a, int b) {
            return find(a) == find(b);
        }
    }


    static int[] stepV(int V, int[] x) {
        int[] next = new int[x.length+1];
        if (V == -1) {
            return next;
        }
        for (int i = 0; i < x.length ; ) {
            int j = i;
            while (j+1 < x.length && x[j+1] - x[j] <= V) {
                j++;
            }
            for (int k = i ; k <= j; k++) {
                next[k] = j+1;
            }
            i = j+1;
        }
        next[x.length] = x.length;
        return next;
    }

    static int[] doit(int V, int[] x) {
        int[] vs = new int[REDUCE];
        Arrays.fill(vs, -1);
        vs[0] = V/2;
        for (int i = 1 ; i < vs.length; i++) {
            vs[i] = vs[i-1] / 2;
            if (vs[i] == 0) {
                break;
            }
        }
        int[][] next = new int[REDUCE][];
        for (int gi = 0 ; gi < next.length ; gi++) {
            int v = vs[gi];
            next[gi] = stepV(v, x);
        }

        int[] dp = new int[1<<REDUCE];
        for (int set = 0; set < dp.length ; set++) {
            for (int i = 0; i < REDUCE ; i++) {
                if ((set & (1<<i)) >= 1) {
                    continue;
                }
                int now = dp[set];
                int ti = set | (1<<i);
                dp[ti] = Math.max(dp[ti], Math.max(now, next[i][now]));
            }
        }
        return dp;
    }

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

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

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

        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() {
            return (char) skipWhileSpace();
        }

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

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            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());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

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