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Ex - Min + Sum

Score : $600$ points

Problem Statement

You are given two sequences of integers of length $N$: $A = (A_1, A_2, \ldots, A_N)$ and $B = (B_1, B_2, \ldots, B_N)$.

Print the number of pairs of integers $(l, r)$ that satisfy $1 \leq l \leq r \leq N$ and the following condition.

• $\min\lbrace A_l, A_{l+1}, \ldots, A_r \rbrace + (B_l + B_{l+1} + \cdots + B_r) \leq S$

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq S \leq 3 \times 10^{14}$
• $0 \leq A_i \leq 10^{14}$
• $0 \leq B_i \leq 10^9$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $S$

$A_1$ $A_2$ $\ldots$ $A_N$

$B_1$ $B_2$ $\ldots$ $B_N$

Output

Print the answer.

4 15
9 2 6 5
3 5 8 9

6

The following six pairs of integers $(l, r)$ satisfy $1 \leq l \leq r \leq N$ and the condition in the problem statement: $(1, 1)$, $(1, 2)$, $(2, 2)$, $(2, 3)$, $(3, 3)$, and $(4, 4)$.

15 100
39 9 36 94 40 26 12 26 28 66 73 85 62 5 20
0 0 7 7 0 5 5 0 7 9 9 4 2 5 2

119