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>
using namespace std;
int main(){
	int N; long long A, B; cin >> N >> A >> B; 
	if(A > B) swap(A, B); 
	long long S[100010] = {}; 
	S[0] = -2e18; 
	for(int i = 1; i <= N; i++) cin >> S[i]; 
	for(int i = 2; i <= N; i++){
		if(S[i] - S[i-2] < A){
			cout << 0 << endl; return 0; 
		}
	}
	int P = 1000000007; 
	int dp[100010] = {}; 
	int DP[100010] = {}; // 累積和
	int L = 0; int R = 0; // 最後にBに割り振った可能性として[L, R)がありうる 
	dp[0] = 1; DP[0] = 1; 
	for(int i = 1; i <= N; i++){
		if(i >= 2 && S[i-1] - S[i-2] < A) L = i-2; // 最後にBに割り振った番号はL以上
		while(R < L || S[i] - S[R] >= B) R++; // 最後にBに割り振った番号はR未満
		dp[i] = P + DP[R-1] - (L > 0 ? DP[L-1] : 0); 
		if(dp[i] >= P) dp[i] -= P; 
		DP[i] = DP[i-1] + dp[i]; 
		if(DP[i] >= P) DP[i] -= P; 
	}
	if(S[N] - S[N-1] < A) L = N-1; 
	int ans = P + DP[N] - (L > 0 ? DP[L-1] : 0); 
	if(ans >= P) ans -= P; 
	cout << ans << endl; 
}