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;

int N, nd[2], bg[2], dp[100009][2], s[100009][2];
long long v[100009], df[2];
const int mod = 1e9 + 7;

int add (int x, int y) {int ans = x + y; if (ans >= mod) ans -= mod; return ans;}
int subtract (int x, int y) {if (x >= y) return x - y; return x - y + mod;}

int main ()
{
scanf ("%d %lld %lld", &N, &df[0], &df[1]);
for (int i=1; i<=N; i++)
    scanf ("%lld", &v[i]), v[N + 1] = 2e18 + v[N];
dp[0][0] = dp[0][1] = s[0][0] = s[0][1] = 1;
for (int i=1; i<=N; i++)
    for (int j=0; j<2; j++)
    {
        while (v[i + 1] - v[nd[j] + 1] >= df[j ^ 1] && nd[j] + 1 < i) nd[j] ++;
        if (i > 1 && v[i] - v[i - 1] >= df[j]) ;
        else bg[j] = i - 1;
        if (bg[j] <= nd[j])
            dp[i][j] = subtract (s[nd[j]][j ^ 1], (bg[j] ? s[bg[j] - 1][j ^ 1] : 0));
        s[i][j] = add (s[i - 1][j], dp[i][j]);
    }
printf ("%d\n", add (dp[N][0], dp[N][1]));
return 0;
}