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

int main() {
    int N;
    cin >> N;
    ll A, B;
    cin >> A >> B;
    if (A > B) swap(A, B);
    vector<ll> S(N);
    for (int i = 0; i < N; i++) cin >> S[i];
    for (int i = 2; i < N; i++) {
        if (S[i]-S[i-2] < A) {
            cout << 0 << endl;
            return 0;
        }
    }
    S.insert(S.begin(), -2e18);
    
    vector<ll> dp(N+2, 0);
    dp[0] = 0;
    dp[1] = 1;
    vector<ll> sum(N+2, 0);
    sum[0] = 0;
    sum[1] = 1;
    int pt = 0;
    
    ll mod = 1e9+7;
    for (int i = 1; i <= N; i++) {
        int lim = distance(S.begin(), lower_bound(S.begin(), S.end(), S[i]-B));
        if (S[lim] > S[i]-B) lim--;
        if (pt <= lim) {
            if (pt >= 0) dp[i+1] = (sum[lim+1]-sum[pt]+mod)%mod;
            else dp[i+1] = sum[lim+1];
        }
        //cout << lim  << " " << dp[i+1] << endl;
        sum[i+1] = (sum[i]+dp[i+1])%mod;
        if (S[i] - S[i-1] < A) {
            pt = i-1;
        }
    }
    cout << (sum[N+1] - sum[pt] + mod) % mod << endl;
    return 0;
}