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문제

당신은 주식을 사고 팔아 이윤을 남기고 싶다. 주식 투자에 대한 법이 최근 바뀌어 아래와 같은 제한이 있다.

  • 시장은 1일차부터 n일차까지, n일 동안만 개장된다.
  • 당신은 그 중에 연속된 k일 (k ≥ 1) 기간 동안에만 참가할 수 있다. 참가하는 날에는 무조건 매일 주식을 사야 한다.
  • 당신이 주식을 살 때의 가격은, 매일 y원으로, 언제나 일정하다.
  • 당신이 주식을 팔 때의 가격은, i일차에 산 경우 V[i]원으로, 산 날짜에 따라 다르다. V[i]는 음수일 수 있다.
  • 당신은 초기 자금 X원을 가지고 참가한다.
  • 당신은 시장 개장 기간인 n일차가 지나기 전까지는 산 주식을 팔 수 없다.
  • 당신은 최소 Z원 이상의 이윤을 남겨야 한다. (Z ≥ 0)

즉, 1 ≤ i ≤ j ≤ n을 만족하는 i일차부터 j일차까지 주식을 샀다면,

(V[i] + V[i+1] + … + V[j-1] + V[j]) - y × (j - i + 1) ≥ Z 및 y × (j - i + 1) ≤ X 을 만족해야 한다.

이 때, 당신의 목표는 Z원 이상의 이윤을 남길 수 있는 구매 방법 중에서 가장 짧은 기간을 찾는 것이다.

다시 말해서, 이윤은 Z원 이상만 남길 수 있다면 아무래도 상관없고, 최대한 짧은 기간 동안에 Z원 이상의 이윤을 남기는 방법을 찾고 싶다. 그러한 기간을 나타내는 시작일/종료일 i, j를 출력하는 프로그램을 만드시오.

동일한 최단 기간 구매법이 복수 존재한다면, 그 중 i가 가장 큰 (즉, 시장에 가장 늦게 진입하는) 기간을 출력하시오.

Z원 이상의 이윤을 남길 수 있는 방법이 존재하지 않는다면, -1을 출력하시오.

입력

첫 줄에 테스트 케이스의 수 T가 주어진다 (1 ≤ T ≤ 10).

각 테스트 케이스는 두 줄에 걸쳐서 주어진다.

첫째 줄에 n, X, y, Z가 공백으로 구분되어 주어진다. 0 ≤ X, y, Z ≤ 109 를 만족한다.

둘째 줄에 n개의 정수 V가 공백으로 구분되어 주어진다. 각 V[i] 는 |V[i]| ≤ 106 를 만족한다.

출력

각 테스트 케이스에 대해 한 줄에 답을 출력한다. 문제에서 언급된 조건들을 만족하는 i, j가 존재하지 않을 경우 -1을 출력하고, 아닌 경우 묘사된대로 (j - i + 1)을 최소화 하는 (i, j) 중 i값이 최대가 되는 i, j 를  공백으로 구분하여 출력한다.

서브태스크 1 (5점)

  • 1 ≤ n ≤ 5,000

서브태스크 2 (11점)

  • 1 ≤ n ≤ 100,000

예제 입력 1

5
1 0 0 1
1
2 0 0 4
1 2
3 0 0 3
2 -1 2
3 0 0 2
2 -1 2
3 0 0 1
2 -1 2

예제 출력 1

1 1
-1
1 3
3 3
3 3
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You must buy a stock everyday (for k consecutive days).<\/li>\r\n\t<li>The buying price for the stock is always fixed: It&#39;s y dollars per day.<\/li>\r\n\t<li>In contrast, the selling price for the stock depends on when you have bought it; It&#39;s V[i] dollars if you have bought it on the day i.<\/li>\r\n\t<li>You start with X dollars as your initial budget.<\/li>\r\n\t<li>You cannot sell stocks before the market is completely closed (after day n).<\/li>\r\n\t<li>You must gain at least Z dollars of profit. 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출처

  • 데이터를 추가한 사람: jame0313

채점 및 기타 정보

  • 예제는 채점하지 않는다.