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(){
    constexpr long MOD = 1000000007;
    size_t N;
    long A, B;
    cin >> N >> A >> B;
    vector<long> dpA(N + 1), dpB(N + 1), val(N + 1);
    val[0] = numeric_limits<long>::min();
    long nA = 0, nB = 0, lA = 0, lB = 0;
    dpA[0] = dpB[0] = 1;
    for(long i = 0; i < N; ++i){
        cin >> val[i + 1];
        while(nA < i && val[nA + 1] + A <= val[i + 1])++nA;
        while(nB < i && val[nB + 1] + B <= val[i + 1])++nB;
        dpA[i + 1] = i ? ((nA == i) * dpA[i] + (lB <= nA) * dpB[min(nA + 1, i)]) % MOD : 1;
        dpB[i + 1] = i ? ((nB == i) * dpB[i] + (lA <= nB) * dpA[min(nB + 1, i)]) % MOD : 1;
        if(val[i + 1] < val[i] + A)lA = i;
        if(val[i + 1] < val[i] + B)lB = i;
    }
    cout << (dpA[N] + dpB[N]) % MOD << endl;
    return 0;
}