문제
이 문제는 출근하기 싫어 2와 굵은 글씨로 적힌 부분과 제한 조건만 다릅니다.
누구나 그렇듯 동우는 출근하기 싫다. 그래도 출근해야 한다.
동우가 다니는 회사는 신기한 회사이다. 총 $N$명의 직원이 있는데, 이 중 최대 1ドル$명이 출근하지 않아도 업무를 정상적으로 진행할 수 있다. 하지만 1ドル$명보다 많이 출근하지 않으면 업무를 정상적으로 진행할 수 없다.
동우는 회사의 업무가 정상적으로 진행되는 것이 신기해 현재 시각으로부터 최근 $M$시간 동안 $N$명의 직원 각각이 총 몇 시간씩 출근했는지 살펴보았다.
직원들은 모두 정각에만 출근해 정각에만 퇴근하며, 한 사람이 여러 번 출근 혹은 퇴근할 수 있다. 최근 $M$시간 동안 업무를 계속 정상적으로 진행할 수 있도록 하는, $N$명의 직원이 출근한 조합의 경우의 수를 구하시오.
이때, $M$시간에 대해 매시 30분을 기준으로 출근해 있는 직원들의 목록이 한 번이라도 다른 경우 서로 다른 조합으로 간주한다. 현재는 정각이라 가정한다.
출력
직원이 출근한 조합으로 가능한 경우의 수를 10ドル^9+7$로 나눈 나머지를 출력한다.
단, 10ドル^9+7$은 소수이다.
서브태스크
| 번호 | 배점 | 제한 | | 1 | 21 | $N\times M \le 20$
|
| 2 | 24 | $N, M \le 6$
|
| 3 | 64 | $N, M \le 1000$
|
| 4 | 71 | 추가적인 제한 조건 없음
|
[{"problem_id":"31537","problem_lang":"0","title":"\ucd9c\uadfc\ud558\uae30 \uc2eb\uc5b4 1","description":"<blockquote>\r\n<p>\uc774 \ubb38\uc81c\ub294 <a href=\"\/problem\/31538\">\ucd9c\uadfc\ud558\uae30 \uc2eb\uc5b4 2<\/a>\uc640 <strong>\uad75\uc740<\/strong> \uae00\uc528\ub85c \uc801\ud78c \ubd80\ubd84\uacfc \uc81c\ud55c \uc870\uac74\ub9cc \ub2e4\ub985\ub2c8\ub2e4.<\/p>\r\n<\/blockquote>\r\n\r\n<p>\ub204\uad6c\ub098 \uadf8\ub807\ub4ef \ub3d9\uc6b0\ub294 \ucd9c\uadfc\ud558\uae30 \uc2eb\ub2e4. \uadf8\ub798\ub3c4 \ucd9c\uadfc\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3d9\uc6b0\uac00 \ub2e4\ub2c8\ub294 \ud68c\uc0ac\ub294 \uc2e0\uae30\ud55c \ud68c\uc0ac\uc774\ub2e4. \ucd1d $N$\uba85\uc758 \uc9c1\uc6d0\uc774 \uc788\ub294\ub370, \uc774 \uc911 <strong>\ucd5c\ub300 $1$\uba85<\/strong>\uc774 \ucd9c\uadfc\ud558\uc9c0 \uc54a\uc544\ub3c4 \uc5c5\ubb34\ub97c \uc815\uc0c1\uc801\uc73c\ub85c \uc9c4\ud589\ud560 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc <strong>$1$\uba85\ubcf4\ub2e4<\/strong> \ub9ce\uc774 \ucd9c\uadfc\ud558\uc9c0 \uc54a\uc73c\uba74 \uc5c5\ubb34\ub97c \uc815\uc0c1\uc801\uc73c\ub85c \uc9c4\ud589\ud560 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ub3d9\uc6b0\ub294 \ud68c\uc0ac\uc758 \uc5c5\ubb34\uac00 \uc815\uc0c1\uc801\uc73c\ub85c \uc9c4\ud589\ub418\ub294 \uac83\uc774 \uc2e0\uae30\ud574 \ud604\uc7ac \uc2dc\uac01\uc73c\ub85c\ubd80\ud130 \ucd5c\uadfc $M$\uc2dc\uac04 \ub3d9\uc548 $N$\uba85\uc758 \uc9c1\uc6d0 \uac01\uac01\uc774 \ucd1d \uba87 \uc2dc\uac04\uc529 \ucd9c\uadfc\ud588\ub294\uc9c0 \uc0b4\ud3b4\ubcf4\uc558\ub2e4.<\/p>\r\n\r\n<p>\uc9c1\uc6d0\ub4e4\uc740 \ubaa8\ub450 \uc815\uac01\uc5d0\ub9cc \ucd9c\uadfc\ud574 \uc815\uac01\uc5d0\ub9cc \ud1f4\uadfc\ud558\uba70, \ud55c \uc0ac\ub78c\uc774 \uc5ec\ub7ec \ubc88 \ucd9c\uadfc \ud639\uc740 \ud1f4\uadfc\ud560 \uc218 \uc788\ub2e4. \ucd5c\uadfc $M$\uc2dc\uac04 \ub3d9\uc548 \uc5c5\ubb34\ub97c \uacc4\uc18d \uc815\uc0c1\uc801\uc73c\ub85c \uc9c4\ud589\ud560 \uc218 \uc788\ub3c4\ub85d \ud558\ub294, $N$\uba85\uc758 \uc9c1\uc6d0\uc774 \ucd9c\uadfc\ud55c \uc870\ud569\uc758 \uacbd\uc6b0\uc758 \uc218\ub97c \uad6c\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc774\ub54c, $M$\uc2dc\uac04\uc5d0 \ub300\ud574 \ub9e4\uc2dc 30\ubd84\uc744 \uae30\uc900\uc73c\ub85c \ucd9c\uadfc\ud574 \uc788\ub294 \uc9c1\uc6d0\ub4e4\uc758 \ubaa9\ub85d\uc774 \ud55c \ubc88\uc774\ub77c\ub3c4 \ub2e4\ub978 \uacbd\uc6b0 \uc11c\ub85c \ub2e4\ub978 \uc870\ud569\uc73c\ub85c \uac04\uc8fc\ud55c\ub2e4. \ud604\uc7ac\ub294 \uc815\uac01\uc774\ub77c \uac00\uc815\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc9c1\uc6d0\uc758 \uc218 $N$\uacfc \ub3d9\uc6b0\uac00 \uc0b4\ud3b4\ubcf8 \ucd5c\uadfc \uc2dc\uac04\uc758 \uae38\uc774\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $M$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1\\le N, M\\le 10^6)$<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 $N$\uba85\uc758 \uc9c1\uc6d0\uc774 \ucd5c\uadfc $M$\uc2dc\uac04 \ub3d9\uc548 \ucd9c\uadfc\ud55c \uc2dc\uac04 $A_1, A_2, \\cdots, A_N$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(0\\le A_i \\le M)$<\/p>\r\n","output":"<p>\uc9c1\uc6d0\uc774 \ucd9c\uadfc\ud55c \uc870\ud569\uc73c\ub85c \uac00\ub2a5\ud55c \uacbd\uc6b0\uc758 \uc218\ub97c $10^9+7$\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e8, $10^9+7$\uc740 \uc18c\uc218\uc774\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","subtask1":"<p>$N\\times M \\le 20$<\/p>\r\n","subtask2":"<p>$N, M \\le 6$<\/p>\r\n","subtask3":"<p>$N, M \\le 1000$<\/p>\r\n","subtask4":"<p>\ucd94\uac00\uc801\uc778 \uc81c\ud55c \uc870\uac74 \uc5c6\uc74c<\/p>\r\n"},{"problem_id":"31537","problem_lang":"1","title":"I don\u2019t wanna go to work 1","description":"<blockquote>\r\n<p>This problem, compared to <a href=\"\/problem\/31538\">I don&rsquo;t wanna go to work 2<\/a>, is the same except for the <strong>bold<\/strong> parts and the&nbsp;constraints of the problem.<\/p>\r\n<\/blockquote>\r\n\r\n<p>Like everyone else, Dongwoo doesn&rsquo;t want to go to work. Still, he must.<\/p>\r\n\r\n<p>Dongwoo&rsquo;s company is a peculiar one. There are a total of $N$ employees, and even if <strong>up to $1$<\/strong> of them doesn&rsquo;t come to work, the company can still carry out its business normally. But if <strong>more than $1$<\/strong> person doesn&rsquo;t come to work, the company cannot carry out its business normally.<\/p>\r\n\r\n<p>Dongwoo, surprised that the company&rsquo;s work was carried out normally in these conditions, looked at how many hours each of the $N$ employees went to work in the last $M$ hours.<\/p>\r\n\r\n<p>Everyone goes to work and gets off work exactly on the hour, and the company was able to carry out its business normally for the last $M$ hours. Given the total number of hours each of the $N$ employees has gone to work in the last $M$ hours, find the number of all possible cases. An employee can go to work or get off work several times.<\/p>\r\n\r\n<p>In the period of $M$ hours, checking every hour at 30 minutes past the hour, if there is at least one time where at least one person who went to work is different, it is a different case. It is assumed that the current time is on the hour.<\/p>\r\n","input":"<p>The first line contains two integers, $N$ and $M$, separated by spaces $(1\\le N,M\\le 10^6)$ &ndash; the number of employees and the length of the recent time Dongwoo looked at.<\/p>\r\n\r\n<p>The second line contains $N$ integers, $A_1,A_2,\\cdots ,A_N$, separated by spaces $(0\\le A_i\\le M)$ &ndash; the time the employees went to work in the last $M$ hours.<\/p>\r\n","output":"<p>Output a single integer &ndash; the remainder of the number of all possible combinations of employees who went to work, divided by $10^9+7$.<\/p>\r\n\r\n<p>Note that $10^9+7$ is a prime number.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","subtask1":"<p>$N\\times M \\le 20$<\/p>\r\n","subtask2":"<p>$N, M \\le 6$<\/p>\r\n","subtask3":"<p>$N, M \\le 1000$<\/p>\r\n","subtask4":"<p>There are no additional restrictions.<\/p>\r\n"}]