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>

typedef long long LL;
const int N = 100005, mod = 1000000007;
const LL inf = 0x3f3f3f3f3f3f3f3f;

void reduce(int &x) { x += x >> 31 & mod; }
int n, dp[N], L[N], sum[N], ans = 0;
LL A, B, x[N];

int main() {
	std::ios::sync_with_stdio(0), std::cin.tie(0);
	std::cin >> n >> A >> B;
	if (A > B) std::swap(A, B);
	x[0] = -inf; for (int i = 1; i <= n; ++i) std::cin >> x[i];
	for (int i = 1; i + 2 <= n; ++i) if (x[i + 2] - x[i] < A)
		return std::cout << "0\n", 0;
	L[1] = 1;
	for (int i = 2; i <= n; ++i)
		L[i] = x[i] - x[i - 1] >= A ? L[i - 1] : i;
	sum[0] = dp[0] = dp[1] = 1, sum[1] = 2; int k = 0;
	for (int i = 2; i <= n; ++i) {
		while (x[i] - x[k + 1] >= B) ++k;
		int l = L[i - 1] - 1, r = k;
		if (l <= r) {
			dp[i] = sum[r]; if (l) reduce(dp[i] -= sum[l - 1]);
		}
		reduce(sum[i] = sum[i - 1] + dp[i] - mod);
	}
	for (int i = L[n] - 1; i <= n; ++i)
		reduce(ans += dp[i] - mod);
	std::cout << ans << '\n';
	return 0;
}