문제
메이플 스토리에는 블레싱 마하, 하울링같이 자신의 공격력을 변화시키는 버프 스킬이 있다. 메이플을 즐겨하는 20년차 고인물 임스는 공격 스킬만 쓰는 메이플에 질려 위의 예시와 같은 버프 스킬을 이용하여 자기만의 독특한 방식으로 보스를 잡아보려고 한다.
임스는 $N$개의 버프 스킬이 있는데, $i$번째 스킬은 공격력을 $a_{i}$ 배로 증가시키고 $b_{i}$ 만큼 더하는 스킬이다. 이때, $b_{i}$가 음수일 수도 있다. 만약 $a_{i} = 3,ドル $b_{i} = 5$이고 현재 공격력이 $x$라면, $i$번 스킬을 사용한 이후에 공격력이 $x\times3+5$로 변경된다. 스킬은 여러 번 사용이 가능하며, 사용한 순서대로 적용된다.
임스는 오늘도 $Q$개의 던전을 깨려고 한다. 각 던전에는 보스가 존재하는데, 보스마다 체력이 다르다. 또한, 보스마다 레벨과 방어율 등이 달라 임스의 초기 공격력은 임스가 상대하는 보스에 따라 다르다.
임스의 공격력이 보스의 체력과 같거나 높아지면 보스를 한 대에 잡을 수 있다. 이때, 단 한 대에 보스를 잡기 위해선 최소 몇 번의 스킬을 사용해야 할까?
출력
각각의 던전마다 보스를 한 대에 잡기 위해 사용해야 하는 최소 스킬 사용 횟수를 한 줄에 하나씩 출력한다.
주어진 스킬로 보스를 한 대에 잡을 수 없는 경우 -1을 출력한다.
[{"problem_id":"29795","problem_lang":"0","title":"\ud55c \ub300","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/2228f651-2ab6-4bcf-8c5a-a9083501bd38\/-\/preview\/\" \/><\/p>\r\n\r\n<p>\uba54\uc774\ud50c \uc2a4\ud1a0\ub9ac\uc5d0\ub294 \ube14\ub808\uc2f1 \ub9c8\ud558, \ud558\uc6b8\ub9c1\uac19\uc774 \uc790\uc2e0\uc758 \uacf5\uaca9\ub825\uc744 \ubcc0\ud654\uc2dc\ud0a4\ub294 \ubc84\ud504 \uc2a4\ud0ac\uc774 \uc788\ub2e4. \uba54\uc774\ud50c\uc744 \uc990\uaca8\ud558\ub294 20\ub144\ucc28 \uace0\uc778\ubb3c \uc784\uc2a4\ub294 \uacf5\uaca9 \uc2a4\ud0ac\ub9cc \uc4f0\ub294 \uba54\uc774\ud50c\uc5d0 \uc9c8\ub824 \uc704\uc758 \uc608\uc2dc\uc640 \uac19\uc740 \ubc84\ud504 \uc2a4\ud0ac\uc744 \uc774\uc6a9\ud558\uc5ec \uc790\uae30\ub9cc\uc758 \ub3c5\ud2b9\ud55c \ubc29\uc2dd\uc73c\ub85c \ubcf4\uc2a4\ub97c \uc7a1\uc544\ubcf4\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc784\uc2a4\ub294 $N$\uac1c\uc758 \ubc84\ud504 \uc2a4\ud0ac\uc774 \uc788\ub294\ub370, $i$\ubc88\uc9f8 \uc2a4\ud0ac\uc740 \uacf5\uaca9\ub825\uc744 $a_{i}$ \ubc30\ub85c \uc99d\uac00\uc2dc\ud0a4\uace0 $b_{i}$ \ub9cc\ud07c \ub354\ud558\ub294 \uc2a4\ud0ac\uc774\ub2e4. \uc774\ub54c, $b_{i}$\uac00 \uc74c\uc218\uc77c \uc218\ub3c4 \uc788\ub2e4. \ub9cc\uc57d $a_{i} = 3$, $b_{i} = 5$\uc774\uace0 \ud604\uc7ac \uacf5\uaca9\ub825\uc774 $x$\ub77c\uba74, $i$\ubc88 \uc2a4\ud0ac\uc744 \uc0ac\uc6a9\ud55c \uc774\ud6c4\uc5d0 \uacf5\uaca9\ub825\uc774 $x\\times3+5$\ub85c \ubcc0\uacbd\ub41c\ub2e4. \uc2a4\ud0ac\uc740 \uc5ec\ub7ec \ubc88 \uc0ac\uc6a9\uc774 \uac00\ub2a5\ud558\uba70, \uc0ac\uc6a9\ud55c \uc21c\uc11c\ub300\ub85c \uc801\uc6a9\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc784\uc2a4\ub294 \uc624\ub298\ub3c4 $Q$\uac1c\uc758 \ub358\uc804\uc744 \uae68\ub824\uace0 \ud55c\ub2e4. \uac01 \ub358\uc804\uc5d0\ub294 \ubcf4\uc2a4\uac00 \uc874\uc7ac\ud558\ub294\ub370, \ubcf4\uc2a4\ub9c8\ub2e4 \uccb4\ub825\uc774 \ub2e4\ub974\ub2e4. \ub610\ud55c, \ubcf4\uc2a4\ub9c8\ub2e4 \ub808\ubca8\uacfc \ubc29\uc5b4\uc728 \ub4f1\uc774 \ub2ec\ub77c \uc784\uc2a4\uc758 \ucd08\uae30 \uacf5\uaca9\ub825\uc740 \uc784\uc2a4\uac00 \uc0c1\ub300\ud558\ub294 \ubcf4\uc2a4\uc5d0 \ub530\ub77c \ub2e4\ub974\ub2e4.<\/p>\r\n\r\n<p>\uc784\uc2a4\uc758 \uacf5\uaca9\ub825\uc774 \ubcf4\uc2a4\uc758 \uccb4\ub825\uacfc \uac19\uac70\ub098 \ub192\uc544\uc9c0\uba74 \ubcf4\uc2a4\ub97c \ud55c \ub300\uc5d0 \uc7a1\uc744 \uc218 \uc788\ub2e4. \uc774\ub54c, \ub2e8 \ud55c \ub300\uc5d0 \ubcf4\uc2a4\ub97c \uc7a1\uae30 \uc704\ud574\uc120 \ucd5c\uc18c \uba87 \ubc88\uc758 \uc2a4\ud0ac\uc744 \uc0ac\uc6a9\ud574\uc57c \ud560\uae4c?<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc2a4\ud0ac\uc758 \uc218 $N$\uacfc \ub358\uc804\uc758 \uc218 $Q$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le N,Q \\le 300\\,000)$<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\ubd80\ud130 $N$\uac1c\uc758 \uc904\uc5d0 $i$\ubc88 \uc2a4\ud0ac\uc758 \uc815\ubcf4\uc778 $a_{i}$, $b_{i}$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le a_{i} \\le 1\\,000\\,000; -10^{9} \\le b_{i} \\le 10^{9})$<\/p>\r\n\r\n<p>\uc774\ud6c4 $Q$\uac1c\uc758 \uc904\uc5d0 $i$\ubc88\uc9f8 \ub358\uc804\uc5d0\uc11c \ucd08\uae30 \uacf5\uaca9\ub825\uc744 \ub098\ud0c0\ub0b4\ub294 $x_{i}$\uc640 \ub358\uc804 \ubcf4\uc2a4\uc758 \uccb4\ub825 $y_{i}$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le x_{i}, y_{i} \\le 10^{12})$<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \ub358\uc804\ub9c8\ub2e4 \ubcf4\uc2a4\ub97c \ud55c \ub300\uc5d0 \uc7a1\uae30 \uc704\ud574 \uc0ac\uc6a9\ud574\uc57c \ud558\ub294 \ucd5c\uc18c \uc2a4\ud0ac \uc0ac\uc6a9 \ud69f\uc218\ub97c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc8fc\uc5b4\uc9c4 \uc2a4\ud0ac\ub85c \ubcf4\uc2a4\ub97c \ud55c \ub300\uc5d0 \uc7a1\uc744 \uc218 \uc5c6\ub294 \uacbd\uc6b0 <span style=\"color:#e74c3c;\"><code>-1<\/code><\/span>\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"29795","problem_lang":"1","title":"One-Hit Kill","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e7c507f4-b14a-4b17-a638-13f95f186d41\/-\/preview\/\" \/><\/p>\r\n\r\n<p>In <em>MapleStory<\/em>, there are buff skills like <em>Maha Blessing<\/em>&nbsp;and <em>Call of the Wild<\/em> that change your attack power. lms0806, a 20-year veteran of <em>MapleStory<\/em>, is tired of using only attack skills. He&nbsp;plans to defeat bosses in a unique way using such buff skills.<\/p>\r\n\r\n<p>lms0806 has $N$ different buff skills. The $i^\\text{th}$ skill increases the attack power by a factor of $a_i$\u200b and then adds $b_i$\u200b to it. Note that $b_i$\u200b can also be negative. If $a_{i}&nbsp;= 3$ and&nbsp;$b_{i} = 5$, and the current attack power is $x$, then after using the $i^\\text{th}$ skill, the attack power becomes $x\\times3+5$. Skills can be used multiple times and are applied in the order used.<\/p>\r\n\r\n<p>lms0806 plans to clear $Q$ dungeons today. Each dungeon has a boss with varying HPs. Additionally, the bosses have different levels and defense rates, so lms0806&#39;s initial attack power varies depending on the boss he is facing.<\/p>\r\n\r\n<p>If lms0806&#39;s&nbsp;attack power equals or exceeds the boss&#39;s HP, he can defeat the boss in one hit. In this case, what is the minimum number of skills that must be used to defeat the boss in a single hit?<\/p>\r\n","input":"<p>The first line contains two integers&nbsp;representing the number of skills $N$ and the number of dungeons $Q$, separated by a space. $(1 \\le N,Q \\le 300\\,000)$<\/p>\r\n\r\n<p>The following&nbsp;$N$ lines contain&nbsp;two integers for each line, providing&nbsp;the details of each skill $a_{i}$ and&nbsp;$b_{i}$, separated by a space.&nbsp;$(1 \\le a_{i}&nbsp;\\le 1\\,000\\,000,&nbsp;-1\\,000\\,000\\,000&nbsp;\\le b_{i} \\le 1\\,000\\,000\\,000)$<\/p>\r\n\r\n<p>The following $Q$ lines contain&nbsp;two integers for each line, providing&nbsp;the&nbsp;initial attack power $x_i$\u200b and the HP of the dungeon boss $y_i$\u200b for the $i^\\text{th}$ dungeon. $(1 \\le x_{i}, y_{i}&nbsp;\\le 10^{12})$<\/p>\r\n","output":"<p>For each dungeon, output the minimum number of skills needed to defeat the boss in one hit on a new line.<\/p>\r\n\r\n<p>If it is impossible to defeat the boss in a single hit with the given skills, output <span style=\"color:#e74c3c;\"><code>-1<\/code><\/span>&nbsp;instead.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]