You have to help a thief to steal as many as GoldCoins as possible from a GoldMine. There he saw N Gold Boxes an each Gold Boxes consists of A_{i} Plates each plates consists of B_{i} Gold Coins. Your task is to print the maximum gold coins theif can steal if he can take a maximum of T plates.

Example 1:
Input:
T = 3, N = 3
A[] = {1, 2, 3}
B[] = {3, 2, 1}
Output:
7
Explanation:
The thief will take 1 plate of coins
from the first box and 2 plate of coins
from the second plate. 3 + 2*2 = 7.
Example 2:
Input:
T = 0, N = 3
A[] = {1, 3, 2}
B[] = {2, 3, 1}
Output:
0
Explanation:
The thief can't take any plates.
So he can't steal any coins.

Your Task:
You don't need to read input or print anything. Your task is to complete the function maxCoins() which takes 2 Integers T, and N and two arrays A and B of size N as input and returns the maximum number of gold coins the thief can steal if he can take a maximum of T plates.

Expected Time Complexity: O(N*logN)
Expected Auxiliary Space: O(N)

Constraints:
0 <= T,N <= 10^{4}
1 <= A[i] <= 10^{4}
1 <= B[i] <= 10^{4}

见题面

见题面