Problem:
Score : 300 points

Problem Statement

We have two desks: A and B. Desk A has a vertical stack of N books on it, and Desk B similarly has M books on it.

It takes us A_i minutes to read the i-th book from the top on Desk A (1 \leq i \leq N), and B_i minutes to read the i-th book from the top on Desk B (1 \leq i \leq M).

Consider the following action:

Choose a desk with a book remaining, read the topmost book on that desk, and remove it from the desk.

How many books can we read at most by repeating this action so that it takes us at most K minutes in total? We ignore the time it takes to do anything other than reading.

Constraints

1 \leq N, M \leq 200000

1 \leq K \leq 10^9

1 \leq A_i, B_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M K
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_M

Output

Print an integer representing the maximum number of books that can be read.

Sample Input 1

3 4 240
60 90 120
80 150 80 150

Sample Output 1

3

In this case, it takes us 60, 90, 120 minutes to read the 1-st, 2-nd, 3-rd books from the top on Desk A, and 80, 150, 80, 150 minutes to read the 1-st, 2-nd, 3-rd, 4-th books from the top on Desk B, respectively.

We can read three books in 230 minutes, as shown below, and this is the maximum number of books we can read within 240 minutes.

Read the topmost book on Desk A in 60 minutes, and remove that book from the desk.

Read the topmost book on Desk B in 80 minutes, and remove that book from the desk.

Read the topmost book on Desk A in 90 minutes, and remove that book from the desk.

Sample Input 2

3 4 730
60 90 120
80 150 80 150

Sample Output 2

7

Sample Input 3

5 4 1
1000000000 1000000000 1000000000 1000000000 1000000000
1000000000 1000000000 1000000000 1000000000

Sample Output 3

0

Watch out for integer overflows.

Solution in OCaml (4.10.0) (judge verdict: Wrong Answer)

open Printf
open Scanf

let id x = x

let n, m, k = scanf "%d %d %d\n" (fun n m k -> n, m, k)
let aa = Array.init n (fun i -> scanf "%d " id)
let bb = Array.init m (fun i -> scanf "%d " id)

exception Break

let main () =
    let ai = ref 0 in
    let bi = ref 0 in
    let result = ref 0 in
    let total = ref 0 in
    try
        while true do
            if !ai < n && !bi < m then begin
                let ta = aa.(!ai) in
                let tb = bb.(!bi) in
                if ta = tb then begin
                    let aii = ref (!ai + 1) in
                    let bii = ref (!bi + 1) in
                    let aIsSmaller = ref true in
                    try
                        while true do 
                            if !aii = n && !bii = m then
                                raise Break
                            else if !aii < n && !bii = m then
                                raise Break
                            else if !aii = n && !bii < m then begin
                                aIsSmaller := false;
                                raise Break
                            end else if aa.(!aii) < bb.(!bii) then
                                raise Break
                            else if aa.(!aii) > bb.(!bii) then begin
                                aIsSmaller := false;
                                raise Break
                            end else begin
                                incr aii;
                                incr bii
                            end
                        done
                    with
                        Break -> begin
                            if !aIsSmaller then begin
                                if !total + ta <= k then begin
                                    total := !total + ta;
                                    incr ai;
                                    incr result
                                end else begin
                                    raise Break
                                end
                            end else begin
                                if !total + tb <= k then begin
                                    total := !total + tb;
                                    incr bi;
                                    incr result
                                end else begin
                                    raise Break
                                end
                            end
                        end
                end else if ta < tb then begin
                    if !total + ta <= k then begin
                        total := !total + ta;
                        incr ai;
                        incr result
                    end else begin
                        raise Break
                    end
                end else begin
                    if !total + tb <= k then begin
                        total := !total + tb;
                        incr bi;
                        incr result
                    end else begin
                        raise Break
                    end
                end
            end else if !ai < n && !bi = m then begin
                let ta = aa.(!ai) in
                if !total + ta <= k then begin
                    total := !total + ta;
                    incr ai;
                    incr result
                end else begin
                    raise Break
                end
            end else if !ai = n && !bi < m then begin
                let tb = bb.(!bi) in
                 if !total + tb <= k then begin
                    total := !total + tb;
                    incr bi;
                    incr result
                end else begin
                    raise Break
                end
            end else begin
                raise Break
            end
        done
    with
        Break ->
            Printf.printf "%d\n" !result

let () = main ()