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>
#define pb push_back
#define fs first
#define sc second
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<double> vd;
typedef pair<int, int> pii;
typedef vector<pii> vpii;

const int N=110000;
const ll P=1e9+7;
ll x[N], xa[N], xb[N], la[N], lb[N];

int main() {
    ll n, a, b, i, ia, ib;
    scanf("%lld%lld%lld", &n, &a, &b);
    for(i=1; i<=n; i++) scanf("%lld", &x[i]);

    for(i=1; i<n; i++) {
        if(x[i+1]-x[i]<a) la[i]=i;
        else la[i]=la[i-1];
        if(x[i+1]-x[i]<b) lb[i]=i;
        else lb[i]=lb[i-1];
    }

    ia=ib=1;
    xa[1]=xb[1]=1;
    for(i=2; i<=n; i++) {
        while(ia+1<=i && x[i]-x[ia]>=a) ia++;
        while(ib+1<=i && x[i]-x[ib]>=b) ib++;

        if(ia==i) xa[i]=(xa[i-1]+xb[i-1])%P;
        else xa[i]=(lb[i-2]<ia? xb[ia] : 0);

        if(ib==i) xb[i]=(xa[i-1]+xb[i-1])%P;
        else xb[i]=(la[i-2]<ib? xa[ib] : 0);
    }
    printf("%lld\n", (xa[n]+xb[n])%P);
    return 0;
}