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;
const int N(111111);
typedef long long LL;
LL s[N];
int modulo(1e9 + 7);
LL inf(2e18);
int c[2][N], dp[2][N], inc[2][N];
int main() {
	int n;
	LL a[2];
	cin >> n >> a[0] >> a[1];
	s[0] = -inf;
	s[n + 1] = inf;
	for(int i(1); i <= n; i++) {
		cin >> s[i];
		for(int d(0); d < 2; d++) {
			c[d][i] = c[d][i - 1] + (s[i] - s[i - 1] >= a[d]);
		}
	}
	dp[0][1] = 1;
	int nxt[2] = {1, 1};
	for(int i(1); i <= n + 1; i++) {
		for(int d(0); d < 2; d++) {
			if(s[i] - s[i - 1] >= a[d ^ 1])
				dp[d][i + 1] = (dp[d][i + 1] + dp[d][i]) % modulo;
			nxt[d] = max(nxt[d], i + 1);
			while(nxt[d] <= n && s[nxt[d]] - s[i - 1] < a[d])
				nxt[d]++;
		}
		for(int d(0); d < 2; d++) {
			if(c[d][nxt[d ^ 1] - 1] - c[d][i] == nxt[d ^ 1] - 1 - i)
				dp[d ^ 1][nxt[d ^ 1]] = (dp[d ^ 1][nxt[d ^ 1]] + dp[d][i]) % modulo;
		}
	}
	cout << (dp[0][n + 1] + dp[1][n + 1]) % modulo << endl;
}