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 = 1e5 + 10;
const long long mod = 1e9 + 7;

long long a[N], dp[N], sum[N];

int main(){
	int n, p, last;
	long long A, B, ans;
	scanf("%d %lld %lld",&n,&A,&B);
	for (int i = 1; i <= n; i++) scanf("%lld",&a[i]);
	if (A < B) swap(A, B);
	for (int i = 3; i <= n; i++){
		if (a[i] - a[i - 2] < B){
			printf("0\n");
			return 0;
		}
	}
	dp[0] = sum[0] = 1; p = last = 0;
	for (int i = 1; i <= n; i++){
		while (p < i - 1 && a[i] - a[p + 1] >= A) p++;
		if (last <= p) dp[i] += (sum[p] - (last ? sum[last - 1] : 0) + mod) % mod;
		sum[i] = (sum[i - 1] + dp[i]) % mod;
		if (i > 1 && a[i] - a[i - 1] < B) last = i - 1; 
	}
	ans = 0;
	for (int i = n; ~i; i--){
		ans += dp[i];
		ans %= mod;
		if (i > 0 && i < n && a[i + 1] - a[i] < B) break;
	}
	printf("%lld\n", ans);
	return 0;
}