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 <algorithm>
#include <cstdio>
#define MOD 1000000007
typedef long long ll;
int dp[100005], sum[100005];
ll arr[100005];
int main()
{
	// freopen("AGC009-C.in", "r", stdin);
	int n;
	ll a, b;
	scanf("%d%lld%lld", &n, &a, &b);
	if (a > b)
		std::swap(a, b);
	arr[0] = -1e18;
	for (int i = 1; i <= n; i++)
	{
		scanf("%lld", arr + i);
		if (i >= 2 && arr[i] - arr[i - 2] < a)
		{
			puts("0");
			return 0;
		}
	}
	dp[0] = sum[1] = 1;
	int l = 0, r = 0;
	for (int i = 1; i <= n; i++)
	{
		while (arr[i] - arr[r] >= b)
			r++;
		dp[i] = (sum[r] - sum[l] + MOD) % MOD;
		sum[i + 1] = (sum[i] + dp[i]) % MOD;
		if (arr[i] - arr[i - 1] < a)
			l = r = i - 1;
	}
	printf("%d\n", (sum[n + 1] - sum[l] + MOD) % MOD);
	return 0;
}