Problem: There is a set consisting of N distinct integers. The i-th smallest element in this set is S_i. We want to divide this set into two sets, X and Y, such that:

* The absolute difference of any two distinct elements in X is A or greater.
* The absolute difference of any two distinct elements in Y is B or greater.



How many ways are there to perform such division, modulo 10^9 + 7? Note that one of X and Y may be empty.

Constraints

* All input values are integers.
* 1 ≦ N ≦ 10^5
* 1 ≦ A , B ≦ 10^{18}
* 0 ≦ S_i ≦ 10^{18}(1 ≦ i ≦ N)
* S_i < S_{i+1}(1 ≦ i ≦ N - 1)

Input

The input is given from Standard Input in the following format:


N A B
S_1
:
S_N


Output

Print the number of the different divisions under the conditions, modulo 10^9 + 7.

Examples

Input

5 3 7
1
3
6
9
12


Output

5


Input

7 5 3
0
2
4
7
8
11
15


Output

4


Input

8 2 9
3
4
5
13
15
22
26
32


Output

13


Input

3 3 4
5
6
7


Output

0

Solution (in JAVA):

Solution:
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/C2";

	FastScanner in;
	PrintWriter out;
	
	long INF = (long)(1e18) + 10L;
	/* MOD_CALCULATION */
	int MOD = 1_000_000_007;
	long ADD(long a, long b) { 
		return (a + b) % MOD;
	}
	
	long SUB(long a, long b) { 
		return (a - b + MOD) % MOD;
	}	

	long MULT(long a, long b) {
		return (a * b) % MOD;
	}

	long POW(long a, long x) {
		long res = 1;
		for ( ; x > 0; x >>= 1) {
			if (x % 2 == 1) res = MULT(res, a);
			a = MULT(a, a);
		}
		
		return res;
	}
	
	long DIV(long a, long b) {
		return MULT(a, POW(b, MOD - 2));
	}
	/* end */
	
	public void solve() {
		int n = in.nextInt();
		long A = in.nextLong(), B = in.nextLong();
		if (A > B) {
			long tmp = A; A = B; B = tmp;
		}
		long[] S = new long[n+1];
		S[0] = -INF;
		for (int i = 1; i <= n; i++) {
			S[i] = in.nextLong();
		}
		for (int i = 0; i <= n - 2; i++) {
			if (S[i+2] - S[i] < A) {
				System.out.println(0);
				return;
			}
		}
		/*
		int minPtr = 0;
		long[] dp = new long[n+1];
		dp[0] = 1;
		for (int i = 0; i < n; i++) {
			// move Y
			for (int j = i; j >= 0; j--) {
				if (S[i+1] - S[j] >= B) 
					dp[i+1] += dp[j];
			}

			// move X
			if (S[i+1] - S[i] < A) {
				while (minPtr < i) dp[minPtr++] = 0;
			}
		}
		*/
		
		int aptr = 0, bptr = 0;
		long cur = 0;
		long[] dp = new long[n+1];
		dp[0] = 1;
		for (int i = 0; i < n; i++) {
			// move Y
			while (S[i+1] - S[bptr] >= B) cur = ADD(cur, dp[bptr++]);
			dp[i+1] = cur;
			
			// move X
			if (S[i+1] - S[i] < A) {
				while (aptr < i) {
					if (aptr < bptr) cur = SUB(cur, dp[aptr]);
					dp[aptr++] = 0;
				}
			}
		}
		
		long res = 0;
		for (int i = 0; i <= n; i++) {
			res = ADD(res, dp[i]);
		}
		System.out.println(res);
	}

	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);
		Thread t = new Thread(null, new Runnable() {

			@Override
			public void run() {
				solve();
			}
		}, "lul", 1 << 30);
		t.start();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(long[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

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

		public FastScanner(InputStream stream) {
			this.stream = stream;
			// stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			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++];
		}

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

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

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

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}