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 fi first
#define se second
typedef pair<int,int> PII;

const long long  MOD = 1e9 + 7;

int n;
long long A, B, dpA[1<<17], dpB[1<<17], s[1<<17], cA[1<<17], cB[1<<17];

int main() {
    cin >> n >> A >> B;
    s[0] = -(1LL<<60);
    for (int i = 1; i <= n; i++) {
        cin >> s[i];
        cA[i] = cA[i-1] + (s[i] < s[i-1] + A);
        cB[i] = cB[i-1] + (s[i] < s[i-1] + B);
    }
    dpA[1] = dpB[1] = 1;
    for (int i = 2, jA = 0, jB = 0; i <= n; i++) {
        while (s[jA+1] + A <= s[i]) jA++;
        if (jA == i-1) dpA[i] = (dpA[i-1] + dpB[i-1]) % MOD;
        else if (cB[i-1] - cB[jA+1] == 0) dpA[i] = dpB[jA+1];

        while (s[jB+1] + B <= s[i]) jB++;
        if (jB == i-1) dpB[i] = (dpA[i-1] + dpB[i-1]) % MOD;
        else if (cA[i-1] - cA[jB+1] == 0) dpB[i] = dpA[jB+1];
    }

    cout << (dpA[n] + dpB[n]) % MOD;
}