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 <cstdio>
#include <algorithm>

using namespace std;

typedef long long ll;

const int MAXN = 1E5 + 10;
const int MOD = 1E9 + 7;

int n;
ll A, B;
ll a[MAXN];
ll f[MAXN][2], s[MAXN][2];

int main(){
	scanf("%d%lld%lld", &n, &A, &B);
	for (int i = 1; i <= n; ++i)
		scanf("%lld", a + i);
	a[0] = -(a[n + 1] = 1ll << 61);
	int la = 1, lb = 1;
	f[0][0] = f[0][1] = 1;
	s[0][0] = s[0][1] = 1;
	for (int i = 1; i <= n; ++i){
		if (a[i] - a[i - 1] < A)
			la = i;
		if (a[i] - a[i - 1] < B)
			lb = i;

		int ra = upper_bound(a, a + i, a[i + 1] - B) - a - 1;
		if (la - 1 <= ra)
			f[i][0] = (s[ra][1] - (la == 1 ? 0 : s[la - 2][1]) + MOD) % MOD;
		int rb = upper_bound(a, a + i, a[i + 1] - A) - a - 1;
		if (lb - 1 <= rb)
			f[i][1] = (s[rb][0] - (lb == 1 ? 0 : s[lb - 2][0]) + MOD) % MOD;
		s[i][0] = (s[i - 1][0] + f[i][0]) % MOD;
		s[i][1] = (s[i - 1][1] + f[i][1]) % MOD;
	}
	printf("%d\n",(int)((f[n][0] + f[n][1]) % MOD));
	return 0;
}