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;
using namespace std;
const ll mod = 1000000007;
const ll mod998 = 998244353;
const ll intmax = 2147483647;
const ll llmax = 9223372036854775807;
const char sp = ' ';

int N, tree[1 << 18], p;
ll A, B, S[100002];

int get(int l, int r, int p, int q, int k) {
	if (q < l || r < p)return 0;
	if (p <= l&&r <= q)return tree[k];
	return (get(l, (l + r) / 2, p, q, k * 2) + get((l + r) / 2 + 1, r, p, q, k * 2 + 1)) % mod;
}

void update(int x, int a) {
	x += (1 << 17);
	while (x) {
		tree[x] += a;
		tree[x] %= mod;
		x /= 2;
	}
}

int main() {
	cin >> N >> A >> B;
	if (A > B)swap(A, B);
	S[0] = -llmax / 3;
	S[N + 1] = llmax / 3;
	for (int i = 1; i <= N; i++) {
		cin >> S[i];
	}
	for (int i = 3; i <= N; i++) {
		if (S[i] - S[i - 2] < A) {
			cout << 0 << endl;
			return 0;
		}
	}
	update(0, 1);
	for (int i = 1; i <= N + 1; i++) {
		update(i, get(0, (1 << 17) - 1, p, upper_bound(S, S + N + 2, S[i] - B) - S - 1, 1));
		if (S[i] - S[i - 1] < A) {
			p = i - 1;
		}
	}
	cout << get(0, (1 << 17) - 1, N + 1, N + 1, 1) << endl;
}