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;

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define FORD(i,b,a) for (int i = (int)(b) - 1; i >= a; --i)
#define REP(i,N) FOR(i,0,N)
#define st first
#define nd second
#define pb push_back

typedef pair<int, int> PII;
typedef long long LL;

const int MOD = 1000000007;

int N;
LL A, B;
LL S[1<<20];

LL DP[1<<20];
LL pref[1<<20];

int main() {
  scanf("%d%lld%lld", &N, &A, &B);
  if (B < A) swap(A, B);

  S[0] = -(1e18+100);
  FOR(i,1,N+1) scanf("%lld", &S[i]);
  S[1+(N++)] = 3e18;

  REP(i,N-2) if (S[i+2] - S[i] < A) {
    printf("0\n");
    return 0;
  }

  DP[0] = 1;

  int a_start = 1;
  FOR(i,1,N+1) {
    pref[i] = (pref[i-1] + DP[i-1]) % MOD;

    int last_good_b = lower_bound(S, S+i, S[i]-B+1) - S - 1;
    int first_good_b = a_start - 1;
    if (first_good_b <= last_good_b) {
      DP[i] = (pref[last_good_b+1] - pref[first_good_b]) % MOD;
    }

    if (S[i] - S[i-1] < A) a_start = i;
  }

  LL result = (DP[N] + MOD) % MOD;
  printf("%lld\n", result);
}