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<stdio.h>
#include<algorithm>
using namespace std;
int n, Near[101000], M;
long long A, B;
long long w[101000], BIT[101000], Mod = 1000000007, D[101000];
void Ins(int a, long long b){
    a++;
    while(a<=M){
        BIT[a] = (BIT[a]+b)%Mod;
        a+=(a&-a);
    }
}
long long Sum(int a){
    long long r = 0;
    a++;
    while(a){
        r = (r+BIT[a])%Mod;
        a-=(a&-a);
    }
    return r;
}
int main(){
    int i, pv = 0, pv2 = 0;
    scanf("%d%lld%lld",&n,&A,&B);
    M = n+2;
    if(A>B)swap(A,B);
    for(i=1;i<=n;i++){
        scanf("%lld",&w[i]);
        if(i>=2 && w[i]-w[i-1] < A) Near[i-1] = 1;
    }
    w[n+1] = 3e18;
    Ins(0,1);
    D[0] = 1;
    for(i=1;i<=n+1;i++){
        while(pv2 + 1 <= i && w[i] - w[pv2+1] >= B) pv2++;
        if(i>=3 && Near[i-2]){
            pv = i-2;
        }
        if(i>=4 && w[i-1] - w[i-3] < A){
            Ins(i-2, Mod-D[i-2]);
        }
        if(pv2 >= pv - 1) D[i] = (Sum(pv2) - Sum(pv - 1) + Mod)%Mod;
        else D[i] = 0;
        Ins(i, D[i]);
    }
    printf("%lld\n",D[n+1]);
}