結果

問題 No.2963 Mecha DESU
コンテスト
ユーザー lif4635
提出日時 2024-11-16 15:50:56
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,150 ms / 2,000 ms
コード長 7,736 bytes
コンパイル時間 514 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 114,524 KB
最終ジャッジ日時 2024-11-16 15:51:52
合計ジャッジ時間 31,942 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 57
権限があれば一括ダウンロードができます

ソースコード

diff # 

"""input"""
#int-input
# input = sys.stdin.readline
def II(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(MI())
#str-input
def SI(): return input()
def MSI(): return input().split()
def SI_L(): return list(SI())
def SI_LI(): return list(map(int, SI()))
#multiple-input
def LLI(n): return [LI() for _ in range(n)]
def LSI(n): return [SI() for _ in range(n)]
#1-indexを0-indexでinput
def MI_1(): return map(lambda x:int(x)-1, input().split())
def TI_1(): return tuple(MI_1())
def LI_1(): return list(MI_1())

from collections import deque,defaultdict,Counter

class dsu():
    n=1
    parent_or_size=[-1 for i in range(n)]
    def __init__(self,N):
        self.n=N
        self.parent_or_size=[-1 for i in range(N)]
    def merge(self,a,b):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        assert 0<=b<self.n, "0<=b<n,b={0},n={1}".format(b,self.n)
        x=self.leader(a)
        y=self.leader(b)
        if x==y:
            return x
        if (-self.parent_or_size[x]<-self.parent_or_size[y]):
            x,y=y,x
        self.parent_or_size[x]+=self.parent_or_size[y]
        self.parent_or_size[y]=x
        return x
    def same(self,a,b):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        assert 0<=b<self.n, "0<=b<n,b={0},n={1}".format(b,self.n)
        return self.leader(a)==self.leader(b)
    def leader(self,a):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        if (self.parent_or_size[a]<0):
            return a
        self.parent_or_size[a]=self.leader(self.parent_or_size[a])
        return self.parent_or_size[a]
    def size(self,a):
        assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
        return -self.parent_or_size[self.leader(a)]
    def groups(self):
        leader_buf=[0 for i in range(self.n)]
        group_size=[0 for i in range(self.n)]
        for i in range(self.n):
            leader_buf[i]=self.leader(i)
            group_size[leader_buf[i]]+=1
        result=[[] for i in range(self.n)]
        for i in range(self.n):
            result[leader_buf[i]].append(i)
        result2=[]
        for i in range(self.n):
            if len(result[i])>0:
                result2.append(result[i])
        return result2
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedSet.py
import math
from bisect import bisect_left, bisect_right
from typing import Generic, Iterable, Iterator, List, Tuple, TypeVar, Optional
T = TypeVar('T')

class SortedSet(Generic[T]):
    BUCKET_RATIO = 16
    SPLIT_RATIO = 24
    
    def __init__(self, a: Iterable[T] = []) -> None:
        "Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)"
        a = list(a)
        n = len(a)
        if any(a[i] > a[i + 1] for i in range(n - 1)):
            a.sort()
        if any(a[i] >= a[i + 1] for i in range(n - 1)):
            a, b = [], a
            for x in b:
                if not a or a[-1] != x:
                    a.append(x)
        n = self.size = len(a)
        num_bucket = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO)))
        self.a = [a[n * i // num_bucket : n * (i + 1) // num_bucket] for i in range(num_bucket)]

    def __iter__(self) -> Iterator[T]:
        for i in self.a:
            for j in i: yield j

    def __reversed__(self) -> Iterator[T]:
        for i in reversed(self.a):
            for j in reversed(i): yield j
    
    def __eq__(self, other) -> bool:
        return list(self) == list(other)
    
    def __len__(self) -> int:
        return self.size
    
    def __repr__(self) -> str:
        return "SortedSet" + str(self.a)
    
    def __str__(self) -> str:
        s = str(list(self))
        return "{" + s[1 : len(s) - 1] + "}"

    def _position(self, x: T) -> Tuple[List[T], int, int]:
        "return the bucket, index of the bucket and position in which x should be. self must not be empty."
        for i, a in enumerate(self.a):
            if x <= a[-1]: break
        return (a, i, bisect_left(a, x))

    def __contains__(self, x: T) -> bool:
        if self.size == 0: return False
        a, _, i = self._position(x)
        return i != len(a) and a[i] == x

    def add(self, x: T) -> bool:
        "Add an element and return True if added. / O(√N)"
        if self.size == 0:
            self.a = [[x]]
            self.size = 1
            return True
        a, b, i = self._position(x)
        if i != len(a) and a[i] == x: return False
        a.insert(i, x)
        self.size += 1
        if len(a) > len(self.a) * self.SPLIT_RATIO:
            mid = len(a) >> 1
            self.a[b:b+1] = [a[:mid], a[mid:]]
        return True
    
    def _pop(self, a: List[T], b: int, i: int) -> T:
        ans = a.pop(i)
        self.size -= 1
        if not a: del self.a[b]
        return ans

    def discard(self, x: T) -> bool:
        "Remove an element and return True if removed. / O(√N)"
        if self.size == 0: return False
        a, b, i = self._position(x)
        if i == len(a) or a[i] != x: return False
        self._pop(a, b, i)
        return True
    
    def lt(self, x: T) -> Optional[T]:
        "Find the largest element < x, or None if it doesn't exist."
        for a in reversed(self.a):
            if a[0] < x:
                return a[bisect_left(a, x) - 1]

    def le(self, x: T) -> Optional[T]:
        "Find the largest element <= x, or None if it doesn't exist."
        for a in reversed(self.a):
            if a[0] <= x:
                return a[bisect_right(a, x) - 1]

    def gt(self, x: T) -> Optional[T]:
        "Find the smallest element > x, or None if it doesn't exist."
        for a in self.a:
            if a[-1] > x:
                return a[bisect_right(a, x)]

    def ge(self, x: T) -> Optional[T]:
        "Find the smallest element >= x, or None if it doesn't exist."
        for a in self.a:
            if a[-1] >= x:
                return a[bisect_left(a, x)]
    
    def __getitem__(self, i: int) -> T:
        "Return the i-th element."
        if i < 0:
            for a in reversed(self.a):
                i += len(a)
                if i >= 0: return a[i]
        else:
            for a in self.a:
                if i < len(a): return a[i]
                i -= len(a)
        raise IndexError
    
    def pop(self, i: int = -1) -> T:
        "Pop and return the i-th element."
        if i < 0:
            for b, a in enumerate(reversed(self.a)):
                i += len(a)
                if i >= 0: return self._pop(a, ~b, i)
        else:
            for b, a in enumerate(self.a):
                if i < len(a): return self._pop(a, b, i)
                i -= len(a)
        raise IndexError
    
    def index(self, x: T) -> int:
        "Count the number of elements < x."
        ans = 0
        for a in self.a:
            if a[-1] >= x:
                return ans + bisect_left(a, x)
            ans += len(a)
        return ans

    def index_right(self, x: T) -> int:
        "Count the number of elements <= x."
        ans = 0
        for a in self.a:
            if a[-1] > x:
                return ans + bisect_right(a, x)
            ans += len(a)
        return ans

# from bisect import bisect_left,bisect_right
n,m,k = MI()
a = LI()

#一回も感電しないゾンビが何を選ばれた時花を考える

cnt = defaultdict(int)
for i in a:
    cnt[i] += 1

t = [0]*(n+1)
for ai,c in cnt.items():
    for j in range(ai,n+1,ai):
        t[j] += c


mod = 998244353
ans = 0
for i in range(1,n+1):
    #もしl種類で感電する時
    p = (m - t[i]) * pow(m,-1,mod)%mod #感電しない確率
    ans += 1 - pow(p,k,mod) #一回以上する確率
    ans %= mod
    # print(ans)

print(ans%mod)
0