Advanced Data Structures, Data Structures, Medium, Segment Trees

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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 \(N \le 2\times 10^5\)

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

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

SAMPLE INPUT

5 6
1 2 3 4 5

SAMPLE OUTPUT

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

Marking Scheme: Marks are awarded when all the testcases pass.

Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), TypeScript, Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, Visual Basic

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All Tracks Data Structures Advanced Data Structures Segment Trees Problem

Advanced Data Structures, Data Structures, Medium, Segment Trees

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