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:

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

import static java.util.Arrays.*;

public class Main {
	private static final int mod = (int)924844033;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			n = io.nextInt();
			V = io.nextInt();
			x = io.nextIntArray(n);
			
			root = new O(0, n, V);
			int d = 0;
			for (int i = V; i > 0; i /= 2) d++;
//			for (O o : root.childs) {
//				dump(root.childs.size(), d, o.l, o.r);
//			}
			d0 = d;
			ans = new boolean[n];
			func();
			for (int i = 0; i < n; i++) {
				io.out.println(ans[i] ? "Possible" : "Impossible");
			}
		}
	}
	
	int d0;
	int n, V;
	int[] x;
	O root;
	Map<Long, Boolean> mp = new HashMap<>();
	boolean func() {
		if (root.childs.size() - 1 > d0) {
			return false;
		}
		List<O> os = new ArrayList<>();
		for (O o : root.childs) os.add(o);
		return func(os, d0 + 1);
	}
	boolean[] ans;
	boolean func(List<O> os, int d) {
		if (os.isEmpty()) return true;
		if (d == 0) return false;

		long h = 0;
		for (O o : os) h += o.hash;
		if (mp.containsKey(h)) return mp.get(h);
		
//		for (O o : os) {
//			dump(os.size(), d, o.l, o.r);
//		}
		
		List<O> oc = new ArrayList<>();
		LOOP: for (O o : os) {
			int size = 0;
			oc.clear();
			for (O t : os) {
				if (o == t) continue;
				size += t.childs.size();
				if (size > d - 1) continue LOOP;
				oc.addAll(t.childs);
			}
			if (func(oc, d - 1)) {
				if (d != d0 + 1) {
					mp.put(h, true);
					return true;
				} else {
					for (int i = o.l; i < o.r; i++) ans[i] = true;
				}
			}
		}
		mp.put(h, false);
		return false;
	}
	
	class O {
		// [l,r)
		int l, r;
		long hash = random.nextLong();
		List<O> childs = new ArrayList<>();
		
		boolean include(int i) { return i >= l && i < r; }
		
		O(int l, int r, int v) {
			this.l = l;
			this.r = r;
			if (v > 0) {
				for (int i = l, j; i < r; i = j) {
					for (j = i + 1; j < r && x[j] - x[j-1] <= v; j++) ;
					childs.add(new O(i, j, v / 2));
				}
			}
		}
	}
	
	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }
	
	void printArrayLn(List<Integer> xs) { for(int i = 0; i < xs.size(); i++) io.out.print(xs.get(i) + (i==xs.size()-1?"\n":" ")); }
	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new Main().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}