문제
경주 연습을 하는 다오
다오는 경주 대회를 열기 위해 $N$개의 트랙을 준비했다. $i$번째로 경주하는 트랙의 길이는 $A_i$이다.
관중들은 트랙의 길이가 점점 길어져야 경주가 재미있다고 생각한다. 즉, $A_1<A_2<\cdots <A_N$인 경우 경주가 재미있다고 생각한다. 이를 위해 다오는 다음과 같은 시행을 0회 이상 할 수 있다.
- 1ドル\le i\le N$인 $i$를 고른 뒤, $i$번째 트랙의 길이를 $K$만큼 늘린다. 즉, $A_i$를 $A_i+K$로 바꾼다.
- 위 시행은 각 $i$에 대해 최대 한 번만 할 수 있다.
다오가 트랙의 길이를 점점 증가하도록 만들 수 있는지 판단하고, 만약 가능하다면 이를 위해 필요한 시행의 최소 횟수를 구하시오.
출력
만약 다오가 트랙의 길이를 점점 증가하도록 만들 수 있다면, 이를 위해 필요한 최소 시행의 횟수를 출력하여라.
만약 다오가 트랙의 길이를 점점 증가하도록 만들 수 없다면, -1을 출력하여라.
제한
- 1ドル\le N\le 10^5$
- 1ドル\le K\le 10^9$
- 0ドル\le A_i\le 10^9$
서브태스크
| 번호 | 배점 | 제한 | | 1 | 10 | $N \le 3$
|
| 2 | 30 | $N \le 10$
|
| 3 | 60 | 문제에 주어진 조건 이외에 추가 제한 조건이 없다.
|
2번과 3번 트랙의 길이를 2ドル$만큼 늘리면 각 트랙의 길이는 $A=[4, 5, 6]$이 되어 트랙의 길이가 점점 길어진다.
트랙의 길이가 점점 증가하도록 트랙의 길이를 늘리는 방법이 존재하지 않는다.
3번, 5번, 6번 트랙의 길이를 5ドル$만큼 늘리면 각 트랙의 길이는 $A=[2, 4, 8, 9, 10, 13]$이 되어 트랙의 길이가 점점 길어진다.
[{"problem_id":"31067","problem_lang":"0","title":"\ub2e4\uc624\uc758 \uacbd\uc8fc \ub300\ud68c","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/u.acmicpc.net\/6a6abcb0-8b58-4642-b89e-014baf5b7713\/kartrider.jpg\" style=\"height: 304px; width: 540px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\uacbd\uc8fc \uc5f0\uc2b5\uc744 \ud558\ub294 \ub2e4\uc624<\/p>\r\n\r\n<p>\ub2e4\uc624\ub294 \uacbd\uc8fc \ub300\ud68c\ub97c \uc5f4\uae30 \uc704\ud574 $N$\uac1c\uc758 \ud2b8\ub799\uc744 \uc900\ube44\ud588\ub2e4. $i$\ubc88\uc9f8\ub85c \uacbd\uc8fc\ud558\ub294 \ud2b8\ub799\uc758 \uae38\uc774\ub294 $A_i$\uc774\ub2e4.<\/p>\r\n\r\n<p>\uad00\uc911\ub4e4\uc740 \ud2b8\ub799\uc758 \uae38\uc774\uac00 \uc810\uc810 \uae38\uc5b4\uc838\uc57c \uacbd\uc8fc\uac00 \uc7ac\ubbf8\uc788\ub2e4\uace0 \uc0dd\uac01\ud55c\ub2e4. \uc989, $A_1&lt;A_2&lt;\\cdots &lt;A_N$\uc778 \uacbd\uc6b0 \uacbd\uc8fc\uac00 \uc7ac\ubbf8\uc788\ub2e4\uace0 \uc0dd\uac01\ud55c\ub2e4. \uc774\ub97c \uc704\ud574 \ub2e4\uc624\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc2dc\ud589\uc744 0\ud68c \uc774\uc0c1 \ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$1\\le i\\le N$\uc778 $i$\ub97c \uace0\ub978 \ub4a4, $i$\ubc88\uc9f8 \ud2b8\ub799\uc758 \uae38\uc774\ub97c $K$\ub9cc\ud07c \ub298\ub9b0\ub2e4. \uc989, $A_i$\ub97c $A_i+K$\ub85c \ubc14\uafbc\ub2e4.<\/li>\r\n\t<li>\uc704 \uc2dc\ud589\uc740 \uac01 $i$\uc5d0 \ub300\ud574 \ucd5c\ub300 \ud55c \ubc88\ub9cc \ud560 \uc218 \uc788\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub2e4\uc624\uac00 \ud2b8\ub799\uc758 \uae38\uc774\ub97c \uc810\uc810 \uc99d\uac00\ud558\ub3c4\ub85d \ub9cc\ub4e4 \uc218 \uc788\ub294\uc9c0 \ud310\ub2e8\ud558\uace0, \ub9cc\uc57d \uac00\ub2a5\ud558\ub2e4\uba74 \uc774\ub97c \uc704\ud574 \ud544\uc694\ud55c \uc2dc\ud589\uc758 \ucd5c\uc18c \ud69f\uc218\ub97c \uad6c\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0\ub294 \ud2b8\ub799\uc758 \uc218 $N$\uacfc \ud2b8\ub799\uc744 \ub298\ub9b4 \uc218 \uc788\ub294 \uae38\uc774 $K$\uac00 \ub744\uc5b4\uc4f0\uae30\ub97c \uc0ac\uc774\uc5d0 \ub450\uace0 \uc815\uc218\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \uac01 \ud2b8\ub799\uc758 \uae38\uc774\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $A_1$, $A_2$, $\\cdots$, $A_N$\uc774 \ub744\uc5b4\uc4f0\uae30\ub97c \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\uc57d \ub2e4\uc624\uac00 \ud2b8\ub799\uc758 \uae38\uc774\ub97c \uc810\uc810 \uc99d\uac00\ud558\ub3c4\ub85d \ub9cc\ub4e4 \uc218 \uc788\ub2e4\uba74, \uc774\ub97c \uc704\ud574 \ud544\uc694\ud55c \ucd5c\uc18c \uc2dc\ud589\uc758 \ud69f\uc218\ub97c \ucd9c\ub825\ud558\uc5ec\ub77c.<\/p>\r\n\r\n<p>\ub9cc\uc57d \ub2e4\uc624\uac00 \ud2b8\ub799\uc758 \uae38\uc774\ub97c \uc810\uc810 \uc99d\uac00\ud558\ub3c4\ub85d \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4\uba74, <code>-1<\/code>\uc744 \ucd9c\ub825\ud558\uc5ec\ub77c.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1\\le N\\le 10^5$<\/li>\r\n\t<li>$1\\le K\\le 10^9$<\/li>\r\n\t<li>$0\\le A_i\\le 10^9$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 3$<\/p>\r\n","subtask2":"<p>$N \\le 10$<\/p>\r\n","subtask3":"<p>\ubb38\uc81c\uc5d0 \uc8fc\uc5b4\uc9c4 \uc870\uac74 \uc774\uc678\uc5d0 \ucd94\uac00 \uc81c\ud55c \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n","sample_explain_1":"<p>2\ubc88\uacfc 3\ubc88 \ud2b8\ub799\uc758 \uae38\uc774\ub97c $2$\ub9cc\ud07c \ub298\ub9ac\uba74 \uac01 \ud2b8\ub799\uc758 \uae38\uc774\ub294 $A=[4, 5, 6]$\uc774 \ub418\uc5b4 \ud2b8\ub799\uc758 \uae38\uc774\uac00 \uc810\uc810 \uae38\uc5b4\uc9c4\ub2e4.<\/p>\r\n","sample_explain_2":"<p>\ud2b8\ub799\uc758 \uae38\uc774\uac00 \uc810\uc810 \uc99d\uac00\ud558\ub3c4\ub85d \ud2b8\ub799\uc758 \uae38\uc774\ub97c \ub298\ub9ac\ub294 \ubc29\ubc95\uc774 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","sample_explain_3":"<p>3\ubc88, 5\ubc88, 6\ubc88 \ud2b8\ub799\uc758 \uae38\uc774\ub97c $5$\ub9cc\ud07c \ub298\ub9ac\uba74 \uac01 \ud2b8\ub799\uc758 \uae38\uc774\ub294 $A=[2, 4, 8, 9, 10, 13]$\uc774 \ub418\uc5b4 \ud2b8\ub799\uc758 \uae38\uc774\uac00 \uc810\uc810 \uae38\uc5b4\uc9c4\ub2e4.<\/p>\r\n"},{"problem_id":"31067","problem_lang":"1","title":"Dao's Racing Competition","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/u.acmicpc.net\/6a6abcb0-8b58-4642-b89e-014baf5b7713\/kartrider.jpg\" style=\"height: 304px; width: 540px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Dao, practicing for his race<\/p>\r\n\r\n<p>Dao prepared $N$ racing tracks to hold a racing competition. The length of the $i$-th racing track is $A_i$.<\/p>\r\n\r\n<p>The spectators think the competition is fun when the lengths of the tracks incrementally increase. In other words, if the condition $A_1&lt;A_2&lt;\\cdots &lt;A_N$ is satisfied, the spectators consider the competition fun. To meet this condition, Dao can apply the following operation any number of times (possibly zero):<\/p>\r\n\r\n<ul>\r\n\t<li>select an index $i$ such that $1\\le i\\le N$ holds, and increase the length of the $i$-th track by $K$. In other words, replace $A_i$ by $A_i+K$.<\/li>\r\n\t<li>Dao can apply the operation above at most once for each $i$.<\/li>\r\n<\/ul>\r\n\r\n<p>Determine if Dao can incrementally increase the length of the track, and if so, find the minimum number of operations required to do so.<\/p>\r\n","input":"<p>The first line contains two integers $N$ and $K$ &mdash; the number of tracks and the length that Dao can increase for each track, separated by a space.<\/p>\r\n\r\n<p>The second line contains integers $A_1$, $A_2$, $\\cdots$, $A_N$ denoting the length of each track, separated by a space.<\/p>\r\n","output":"<p>If Dao can incrementally increase the lengths of the tracks, print the minimum number of operations required for Dao.<\/p>\r\n\r\n<p>If Dao cannot make the lengths of the tracks incrementally increase, print <code>-1<\/code>.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1\\le N\\le 10^5$<\/li>\r\n\t<li>$1\\le K\\le 10^9$<\/li>\r\n\t<li>$0\\le A_i\\le 10^9$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 3$<\/p>\r\n","subtask2":"<p>$N \\le 10$<\/p>\r\n","subtask3":"<p>There are no additional constraints.<\/p>\r\n","sample_explain_1":"<p>If you increase the second and third track lengths by $2$, the lengths of each track become $A=[4,5,6]$, which are incrementally increasing.<\/p>\r\n","sample_explain_2":"<p>There is no way to increase&nbsp;lengths of tracks&nbsp;so that they are incrementally increasing.<\/p>\r\n","sample_explain_3":"<p>If you increase the lengths of the third, fifth, and sixth tracks by $5$, the lengths of each track become $A=[2,4,8,9,10,13]$, which are incrementally increasing.<\/p>\r\n"}]