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 <algorithm>
#include <iostream>
#include <cstdio>
using namespace std;
typedef long long i64;
const int MAXN = 1e5 + 10;
const int MOD = 1e9 + 7;

int N;
i64 S[MAXN];
i64 A, B;
i64 dp[MAXN];

int main()
{
	i64 last = 0, answer = 0;
	int ansptr = 0;

	S[0] = -1LL << 60 ;
	cin >> N >> A >> B ;

	if(A < B)
		swap(A, B);

	dp[0] = 1;
	for(int i = 1, j = 0; i <= N; i++)
	{
		cin >> S[i];
		if(i > 1 && S[i] - S[i-2] < B)
		{
			puts("0");
			return 0;
		}

		while(S[i] - S[j] >= A)
			last = (last + dp[j]) % MOD, j++;
		dp[i] = last;

		if(S[i] - S[i-1] < B)
			j = ansptr = i - 1, last = 0;
	}

	while(ansptr <= N)
		answer = (answer + dp[ansptr]) % MOD, ansptr++;

	cout << answer << endl ;

	return 0;
}