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;

const int Mod = 1e9+7, Nmax = 1e5+5;

int i, p, n, p1=1, p2=1, d[Nmax][2], is_good[Nmax];
long long A, B, a[Nmax];

void get(int p)
{
    while(a[p1] + A <= a[p]) ++p1;
    while(a[p2] + B <= a[p]) ++p2;
}

int main()
{
    // freopen("input", "r", stdin);
  //  freopen("output", "w", stdout);

    scanf("%d%lld%lld", &n, &A, &B);

    if(A>B) swap(A, B);

    for(i=1; i<=n; ++i) scanf("%lld", &a[i]);

    is_good[1] = 1;
    for(i=2; i<=n; ++i)
        if(a[i] - a[i-1] >= A) is_good[i] = is_good[i-1];
        else is_good[i] = i;


    d[1][0] = d[1][1] = 1;

    for(i=2; i<=n; ++i)
    {
        if(a[i] - a[i-1] < A)
            d[i][0] = d[i-1][1] * (a[i] - a[i-2] >= A || i==2);
        else d[i][0] = d[i-1][0] + d[i-1][1];

        get(i);

        if(a[i] - a[i-1] < B)
            d[i][1] = d[p2][0] * (is_good[i-1] <= p2);
        else d[i][1] = d[i-1][1] + d[i-1][0];

        d[i][0] %= Mod;
        d[i][1] %= Mod;
    }

    printf("%d\n", (d[n][0] + d[n][1]) % Mod);

    return 0;
}