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Counting the number of intervals

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You are given a sequence of \(N\) integers \(a_1, a_2, \dots, a_N\) and an integer \(K\). Your task is to count the number of intervals \([l, r] \) such that \(a_l + a_r + min(a_l, a_{l + 1}, \dots, a_r) \le K\).

**Input format**

- First line: Two space-separated integers \(N, K\)
- Second line: \(N\) space-separated integers denoting the elements of the sequence

**Output format**

- Print the answer in a single line.

**Constraints**

**\(1 \le N \le 5\times10^5\)**, \(80\%\) test cases \(N \le 2\times 10^5\)

**\(1 \le K \le 10^{18}\)**

**\(1 \le a_i \le 10^{18}\)**

Explanation

There are five intervals satisfy the condition:

- [1, 1]: \(a_1 + min(a_1) + a_1 = 3\)
- [1, 2]: \(a_1 + min(a_1, a_2) + a_2 = 4\)
- [1, 3]: \(a_1 + min(a_1, a_2, a_3) + a_3 = 5\)
- [1, 4]: \(a_1 + min(a_1, a_2, a_3, a_4) + a_4 = 6\)
- [2, 2]: \(a_2 + min(a_2, a_2) + a_2 = 6\)

Time Limit:
3.0 sec(s)
for each input file.

Memory Limit:
512 MB

Source Limit:
1024 KB

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