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;

const ll mod = 1e9+7;

ll K[101010], S[101010], T[101010];
ll dp[101010][2];
ll n, a, b, s;

void add(ll l, ll r, ll v)
{
	if(l <= r){
		T[l] += v;
		T[r+1] -= v;
	}
}

int main()
{
	ll i, j;
	
	scanf("%lld%lld%lld", &n, &a, &b);
	
	if(a < b) swap(a, b);
	
	for(i=1;i<=n;i++) scanf("%lld", S+i);
	
	if(n == 1){
		printf("2\n");
		return 0;
	}
	
	for(i=n;i>=1;i--){
		if(i == n || S[i+1] - S[i] < b) K[i] = i;
		else K[i] = K[i+1];
	}
	
	add(1, K[1]+1, 1);
	
	for(i=j=1;i<=n;i++){
		for(;j<=n && S[j] - S[i] < a;j++);
		
		s = (s + T[i] + mod) % mod;
		
		if(i == 1){
			add(max(i+2, j), K[i+1]+1, 1);
		}
		else if(i == 2){
			dp[2][0] = (S[2] - S[1] >= a);
			dp[2][1] = 1;
			
			add(max(i+2, j), K[i+1]+1, dp[i][0]);
			if(i < n && S[i+1] - S[i-1] >= b) add(max(i+2, j), K[i+1]+1, dp[i][1]);
		}
		else{
			dp[i][0] = (dp[i-1][0] + dp[i-1][1]) * (S[i] - S[i-1] >= a) % mod;
			dp[i][1] = s;
			
			add(max(i+2, j), K[i+1]+1, dp[i][0]);
			if(i < n && S[i+1] - S[i-1] >= b) add(max(i+2, j), K[i+1]+1, dp[i][1]);
		}
	}
	
	printf("%lld\n",((s + T[i] + dp[n][0] + dp[n][1]) % mod + mod) % mod);
	
	return 0;
}