Meaningful Mean

You are given an integer sequence of length N, a = {a_1, a_2, …, a_N}, and an integer K.

a has N(N+1)/2 non-empty contiguous subsequences, {a_l, a_{l+1}, …, a_r} (1 ≤ l ≤ r ≤ N). Among them, how many have an arithmetic mean that is greater than or equal to K?

Constraints

• All input values are integers.
• 1 ≤ N ≤ 2 \times 10^5
• 1 ≤ K ≤ 10^9
• 1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N K a_1 a_2 : a_N

Output

Print the number of the non-empty contiguous subsequences with an arithmetic mean that is greater than or equal to K.

Examples

Input

3 6 7 5 7

Output

5

Input

1 2 1

Output

0

Input

7 26 10 20 30 40 30 20 10

Output

13

inputFormat

input values are integers.

• 1 ≤ N ≤ 2 \times 10^5
• 1 ≤ K ≤ 10^9
• 1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N K a_1 a_2 : a_N

outputFormat

Output

Print the number of the non-empty contiguous subsequences with an arithmetic mean that is greater than or equal to K.

Examples

Input

3 6 7 5 7

Output

5

Input

1 2 1

Output

0

Input

7 26 10 20 30 40 30 20 10

Output

13

样例

1 2
1

0