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.

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

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.

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.

Sample Input 1

4 15
9 2 6 5
3 5 8 9

Sample Output 1

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).

Sample Input 2

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

Sample Output 2

119

见题面 Input 部分

见题面 Output 部分