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 finish(x) return cout << x << endl, 0
#define ll long long

const int N = 100001;

int n, dp[N], cnt[N], mod = 1e9 + 7;
ll A, B;
vector <ll> a;

int solve(int idx){
    if(idx == n) return 1;
    int &ret = dp[idx];
    if(ret != -1) return ret;
    ret = 0;
    int j = lower_bound(a.begin(), a.end(), a[idx] + A) - a.begin();
    bool ok = (idx == 0 || idx == n - 1 || a[idx + 1] - a[idx - 1] >= B);
    if(idx + 2 < j){
        ok &= cnt[j - 1] - cnt[idx + 1] == j - idx - 2;
    }
    if(ok) ret = solve(j);
    if(idx == 0 || a[idx] - a[idx - 1] >= B){
        ret += solve(idx + 1);
        if(ret >= mod) ret -= mod;
    }
    return ret;
}
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    memset(dp, -1, sizeof dp);
    cin >> n >> A >> B;
    if(A < B) swap(A, B);
    a.resize(n);
    for(auto &i : a) cin >> i;
    for(int i = 1 ; i < n ; i++){
        cnt[i] = cnt[i - 1] + (a[i] - a[i - 1] >= B);
    }
    cout << solve(0) << endl;
}