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 CPP):

Solution:
#include <bits/stdc++.h>

#define F(i, a, b) for (LL i = a; i <= b; i ++)
#define G(i, a, b) for (LL i = a; i >= b; i --)
#define add(a, b) ((a) = (a + b) % Mo)

typedef long long LL;
 
const LL N = 1e5 + 10;
const LL Mo = 1e9 + 7;
const LL inf = 5e18;

using namespace std;

LL n, A, B, L1,R1, L2,R2;
LL S[N], f[N][2], S0[N],S1[N];

int main() {	
	scanf("%lld %lld %lld", &n, &A, &B);
	F(i, 1, n) scanf("%lld", &S[i]);
	sort(S + 1, S + n + 1);
	S[n + 1] = inf, S[0] = - inf;
	S0[0] = S1[0] = f[0][0] = f[0][1] = 1;
	F(i, 1, n) {
		// Update f[i][0]
		while (R1 < i - 1 && S[R1 + 1] <= S[i + 1] - B)
			R1 ++;
		if (S[i] - A < S[i - 1])
			L1 = i - 1;
		if (R1 >= L1) add(f[i][0], S1[R1] - (L1 ? S1[L1 - 1] : 0));
		// Update f[i][1]
		
		while (R2 < i - 1 && S[R2 + 1] <= S[i + 1] - A)
			R2 ++;
		if (S[i] - B < S[i - 1])
			L2 = i - 1;
		if (R2 >= L2) add(f[i][1], S0[R2] - (L2 ? S0[L2 - 1] : 0));
			
		S1[i] = (S1[i - 1] + f[i][1]) % Mo;
		S0[i] = (S0[i - 1] + f[i][0]) % Mo;
	}
	printf("%lld\n", ((f[n][0] + f[n][1]) % Mo + Mo) % Mo);
}