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:
// Crt. 2019-12-06  20:33:58
#include <algorithm>
#include <iostream>
#include <cstdio>
#define N 200005
using namespace std;
typedef long long ll;
const int Mod = 1e9 + 7;

int n, m, f[N], sum[N];
ll A, B, s[N], p[N];

int main() {
#ifdef LOCAL_JUDGE
    freopen("work.in", "r", stdin);
    freopen("work.out", "w", stdout);
#endif

    cin >> n >> A >> B;

    for (int i = 1; i <= n; ++i)
        scanf("%lld", s + i);

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

    for (int i = 2; i < n; ++i)
        if (s[i + 1] - s[i - 1] < B) return puts("0"), 0;

    for (int i = 1; i < n; ++i)
        if (s[i + 1] - s[i] < B) p[++m] = i;


    s[++n] = 4e18;
    f[0] = sum[0] = 1;

    for (int i = 1, posl = 0; i <= n; ++i) {
        int posr = upper_bound(s + 1, s + n + 1, s[i] - A) - s - 1;
        //cout << i << " " << posl << " " << posr << "  ";

        if (posr >= posl)
            f[i] = (sum[posr] + Mod - (posl ? sum[posl - 1] : 0)) % Mod;
        sum[i] = (sum[i - 1] + f[i]) % Mod;

        if (i > 1 && s[i] - s[i - 1] < B) posl = i - 1;

        //cout << f[i] << " " << sum[i] << endl;
    }

    cout << f[n] << endl;

    return 0;
}