Contest Duration: - (local time) (100 minutes) Back to Home
Ex - Min + Sum /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

2 つの長さ N の整数列 A = (A_1, A_2, \ldots, A_N) および B = (B_1, B_2, \ldots, B_N) が与えられます。

1 \leq l \leq r \leq N を満たす整数の組 (l, r) であって下記の条件を満たすものの個数を出力してください。

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

### 制約

• 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
• 入力はすべて整数

### 入力

N S
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_N


### 入力例 1

4 15
9 2 6 5
3 5 8 9


### 出力例 1

6


1 \leq l \leq r \leq N を満たす整数の組 (l, r) であって問題文中の条件を満たすものは、 (1, 1), (1, 2), (2, 2), (2, 3), (3, 3), (4, 4)6 個です。

### 入力例 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


### 出力例 2

119


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


### 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