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 rep(i, l, r) for(int i = (l), i##end = (r);i <= i##end;++i)
using std::cin; using std::cout;
const int maxn = 200200;
typedef long long ll;
const int mod = 1e9 + 7;
inline void reduce(int & x){ x += x >> 31 & mod; }
int n;
ll s[maxn], a, b;
int dp[maxn], pre[maxn], left[maxn];
int main() {
	std::ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	cin >> n >> a >> b;
	if(a > b) std::swap(a, b);
	rep(i, 1, n) cin >> s[i];
	std::sort(s + 1,s + n + 1);
	rep(i, 3, n) if(s[i - 2] + a > s[i]) return cout << 0 << '\n', 0;
	rep(i, 1, n) left[i] = i != 1 && s[i] - s[i - 1] >= a ? left[i - 1] : i;
	dp[0] = dp[1] = pre[0] = 1, pre[1] = 2;
	rep(i, 2, n) {
		int r = std::upper_bound(s + 1,s + i, s[i] - b) - s - 1, l = left[i - 1];
		if(l - 2 <= r)
			reduce(dp[i] = pre[r] - pre[l - 2]);
		reduce(pre[i] = pre[i - 1] + dp[i] - mod);
	}
	int ans = pre[n] - pre[left[n] - 2];
	cout << ans + (ans >> 31 & mod) << '\n';
}