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;
typedef long long ll;

const int MAXN = 100005;
const ll MOD = 1000000007;


ll s[MAXN];
ll prefx[MAXN];
ll prefy[MAXN];
ll dpx[MAXN];
ll dpy[MAXN];

int main()
{
    int n;
    ll A, B;
    cin >> n >> A >> B;
    for (int i = 1; i <= n; i++)
    {
        cin >> s[i];
    }

    int lx = 0;
    int rx = 0;
    int ly = 0;
    int ry = 0;

    dpx[0] = 1;
    dpy[0] = 1;

    prefx[1] = 1;
    prefy[1] = 1;

    for (int i = 1; i <= n-1; i++)
    {
        while (s[i+1] - s[rx] >= B && rx < i) rx++;
        while (s[i+1] - s[ry] >= A && ry < i) ry++;
        rx--; ry--;
        rx = max(0, rx); rx = max(lx-1, rx);
        ry = max(0, ry); ry = max(ly-1, ry);
        dpx[i] = (prefy[ry+1] - prefy[ly] + MOD) % MOD;
        dpy[i] = (prefx[rx+1] - prefx[lx] + MOD) % MOD;

        prefx[i+1] = (prefx[i] + dpx[i]) % MOD;
        prefy[i+1] = (prefy[i] + dpy[i]) % MOD;

        if (s[i+1] - s[i] < A) lx = i;
        if (s[i+1] - s[i] < B) ly = i;

    //    cout << dpx[i] << " " << dpy[i] << endl;
    }

    cout << (prefx[n] - prefx[lx] + prefy[n] - prefy[ly] + 2*MOD) % MOD;

    return 0;
}