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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
long long N, A, B, S[120000], dp[120000][2], mod = 1000000007; vector<long long>EA, EB;
int main() {
	cin >> N >> A >> B; S[1] = -(1LL << 62); S[N + 2] = (1LL << 62); EA.push_back(2); EB.push_back(2);
	for (int i = 2; i <= N + 1; i++) {
		cin >> S[i]; if (S[i] - S[i - 1] < A)EA.push_back(i); if (S[i] - S[i - 1] < B)EB.push_back(i);
	}
	dp[1][0] = 1; dp[1][1] = 1;
	for (int i = 2; i <= N + 1; i++) {
		int pos1 = upper_bound(S, S + N + 3, S[i + 1] - A) - S; pos1--; if (pos1 == i)pos1--;
		int pos2 = upper_bound(EB.begin(), EB.end(), i) - EB.begin(); pos2--; pos2 = EB[pos2] - 1;
		if (pos1 >= pos2)dp[i][0] = (dp[pos1][1] - dp[pos2 - 1][1] + mod) % mod; dp[i][0] += dp[i - 1][0]; dp[i][0] %= mod;
		
		int pos3 = upper_bound(S, S + N + 3, S[i + 1] - B) - S; pos3--; if (pos3 == i)pos3--;
		int pos4 = upper_bound(EA.begin(), EA.end(), i) - EA.begin(); pos4--; pos4 = EA[pos4] - 1;
		if (pos3 >= pos4)dp[i][1] = (dp[pos3][0] - dp[pos4 - 1][0] + mod) % mod; dp[i][1] += dp[i - 1][1]; dp[i][1] %= mod;
	}
	cout << (dp[N + 1][0] + dp[N + 1][1] - dp[N][0] - dp[N][1] + mod * 2) % mod << endl;
	return 0;
}