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;
#define LL long long
const int N = 200000;
const LL INF = 3e18;
const int MOD = 1e9 + 7;
int n; LL a, b;
LL si[N];
int pA[N], pB[N];
int main()
{
    cin >> n >> a >> b;
    for (int i = 1; i <= n; ++ i) cin >> si[i];
    si[0] = -INF; si[n + 1] = INF;
    pA[1] = pB[1] = 1;
    for (int i = 2, lA = 1, rA = 1, lB = 1, rB = 1; i <= n + 1; ++ i)
    {
        while (si[i] - si[rA] >= a && rA < i - 1) rA ++;
        if (si[i - 1] - si[i - 2] < b) lA = i - 1;
        while (si[i] - si[rB] >= b && rB < i - 1) rB ++;
        if (si[i - 1] - si[i - 2] < a) lB = i - 1;
        pA[i] = (0ll + pA[i - 1] + (lA <= rA? pB[rA] - pB[lA - 1]: 0) + MOD) % MOD;
        pB[i] = (0ll + pB[i - 1] + (lB <= rB? pA[rB] - pA[lB - 1]: 0) + MOD) % MOD;
    }
    cout << (0ll + pA[n + 1] - pA[n] + pB[n + 1] - pB[n] + 2ll * MOD) % MOD << endl;
}