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 <cstdio>
#pragma warning(disable : 4996)
int N, ca, cb, sa, sb, la, lb, ret, dpa[100009], dpb[100009], mod = 1000000007; long long A, B, x[100009];
int main() {
	scanf("%d%lld%lld", &N, &A, &B);
	for (int i = 1; i <= N; i++) scanf("%lld", &x[i]);
	dpa[0] = 1; dpb[0] = 1; x[0] = -(1LL << 61);
	for (int i = 1; i < N; i++) {
		while (ca != i && x[ca] + A <= x[i + 1]) {
			sa += (ca >= lb ? dpb[ca] : 0); ca++;
			if (sa >= mod) sa -= mod;
		}
		dpa[i] = sa;
		while (cb != i && x[cb] + B <= x[i + 1]) {
			sb += (cb >= la ? dpa[cb] : 0); cb++;
			if (sb >= mod) sb -= mod;
		}
		dpb[i] = sb;
		if (x[i] + A > x[i + 1]) la = i, sb = 0;
		if (x[i] + B > x[i + 1]) lb = i, sa = 0;
	}
	for (int i = la; i < N; i++) ret = ret + dpa[i] - (ret + dpa[i] < mod ? 0 : mod);
	for (int i = lb; i < N; i++) ret = ret + dpb[i] - (ret + dpb[i] < mod ? 0 : mod);
	printf("%d\n", ret);
	return 0;
}