9169: ABC282 —— Ex - Min + Sum
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Description
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.
- $\min\lbrace A_l, A_{l+1}, \ldots, A_r \rbrace + (B_l + B_{l+1} + \cdots + B_r) \leq S$
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:
```
$N$ $S$
$A_1$ $A_2$ $\ldots$ $A_N$
$B_1$ $B_2$ $\ldots$ $B_N$
```
```
$N$ $S$
$A_1$ $A_2$ $\ldots$ $A_N$
$B_1$ $B_2$ $\ldots$ $B_N$
```
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.
- $0 \leq S \leq 3 \times 10^{14}$
- $0 \leq A_i \leq 10^{14}$
- $0 \leq B_i \leq 10^9$
- All values in the input are integers.
Sample 1 Input
4 15
9 2 6 5
3 5 8 9
Sample 1 Output
6
The following six pairs of integers (l,r) satisfy 1≤l≤r≤N and the condition in the problem statement: (1,1), (1,2), (2,2), (2,3), (3,3), and (4,4).
Sample 2 Input
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 2 Output
119