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.

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