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 MAXN (100010)
#define mod (1000000007)
#define ll long long

int n;
ll A, B, s[MAXN];
int dpx[MAXN], prex[MAXN];
int dpy[MAXN], prey[MAXN];
std::map<ll, int> map;

int main(){
	scanf("%d%lld%lld", &n, &A, &B);
	for(int i = 1; i <= n; ++ i){
		scanf("%lld", s + i);
		map[- s[i]] = i;
	}
	dpx[0] = prex[0] = 1;
	dpy[0] = prey[0] = 1;
	int now1 = 0, now2 = 0;
	for(int i = 2; i <= n; ++ i){
		auto u = map.lower_bound(B - s[i]);
		int sit = u == map.end() ? 0 : u -> second;
		if(sit == i - 1) -- sit;
		dpy[i - 1] = prex[sit];
		
		u = map.lower_bound(A - s[i]);
		sit = u == map.end() ? 0 : u -> second;
		if(sit == i - 1) -- sit;
		dpx[i - 1] = prey[sit];
		
		if(s[i] - s[i - 1] < B){
			for(int j = now1; j < i - 1; ++ j){
				dpy[j] = prey[j] = 0;
			}
			now1 = i - 1;
		}
		
		if(s[i] - s[i - 1] < A){
			for(int j = now2; j < i - 1; ++ j){
				dpx[j] = prex[j] = 0;
			}
			now2 = i - 1;
		}
		
		prey[i - 1] = (prey[i - 2] + dpy[i - 1]) % mod;
		prex[i - 1] = (prex[i - 2] + dpx[i - 1]) % mod;
	}
	printf("%d\n", (prex[n - 1] + prey[n - 1]) % mod);
	return 0;
}