結果

問題 No.3022 一元一次式 mod 1000000000
ユーザー lif4635
提出日時 2025-02-14 22:06:52
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 248 ms / 2,000 ms
コード長 4,881 bytes
コンパイル時間 470 ms
コンパイル使用メモリ 82,548 KB
実行使用メモリ 78,696 KB
最終ジャッジ日時 2025-02-17 12:56:50
合計ジャッジ時間 2,531 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
other AC * 21
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ソースコード

diff #
プレゼンテーションモードにする

# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]
def graph(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[int]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b = map(int, input().split())
        a += index
        b += index
        edge[a].add(b)
        if not dir:
            edge[b].add(a)
    return edge
def graph_w(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[tuple]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b,c = map(int, input().split())
        a += index
        b += index
        edge[a].add((b,c))
        if not dir:
            edge[b].add((a,c))
    return edge
mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
def acc(a:list[int]):
    sa = [0]*(len(a)+1)
    for i in range(len(a)):
        sa[i+1] = a[i] + sa[i]
    return sa
prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')
from collections import defaultdict
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right
def primefact(n:int) -> dict[int,int]:
    p = 2
    res = DD(int)
    while p*p <= n:
        cnt = 0
        while n%p == 0:
            n //= p
            cnt += 1
        if cnt:
            res[p] = cnt
        p += 1
    if n != 1:
        res[n] = 1
    return res
from math import gcd
p2 = 2**9
p5 = 5**9
p = 10**9
def calc2(x):
    c = 0
    while x%2 == 0:
        x //= 2
        c += 1
    return c
def calc5(x):
    c = 0
    while x%5 == 0:
        x //= 5
        c += 1
    return c
def solve2(p,n,m):
    n %= p
    m %= p
    if n == 0:
        if m == 0:
            print(1)
        else:
            print(-1)
        return
    
    if m == 0:
        c2n = calc2(n)
        
        r = 2**max(0,9-c2n)
        print(r)
        return
    
    # そうでない時
    c2n = calc2(n)
    c2m = calc2(m)
    
    # これでそれぞれnについては9未満
    if c2n > c2m:
        print(-1)
        return
    
    g = 2**c2n 
    p //= g
    n //= g
    m //= g
    
    # nには素因数としてn,mがない
    t = pow(-n,-1,p) * m % p
    print(t)
    return
def solve5(p,n,m):
    n %= p
    m %= p
    if n == 0:
        if m == 0:
            print(1)
        else:
            print(-1)
        return
    
    if m == 0:
        c5n = calc5(n)
        r = 5**max(0,9-c5n)
        print(r)
        return
    
    # そうでない時
    c5n = calc5(n)
    c5m = calc5(m)
    
    # これでそれぞれnについては9未満
    if c5n > c5m:
        print(-1)
        return
    
    g = 5**c5n
    p //= g
    n //= g
    m //= g
    
    # nには素因数としてn,mがない
    t = pow(-n,-1,p) * m % p
    print(t)
    return
def solve(p):
    n,m = MI()
    n %= p
    m %= p
    if n == 0:
        if m == 0:
            print(1)
        else:
            print(-1)
        return
    
    if m == 0:
        c2n = calc2(n)
        c5n = calc5(n)
        r = 2**max(0,9-c2n)
        r *= 5**max(0,9-c5n)
        print(r)
        return
    
    # そうでない時
    c2n = calc2(n)
    c5n = calc5(n)
    c2m = calc2(m)
    c5m = calc5(m)
    
    if c2n >= 9:
        if c2m >= 9:
            solve5(p5,n,m)
        else:
            print(-1)
        return
    
    if c5n >= 9:
        if c5m >= 9:
            solve2(p2,n,m)
        else:
            print(-1)
        return
    
    # これでそれぞれnについては9未満
    if c2n > c2m or c5n > c5m:
        print(-1)
        return
    
    g = 2**c2n
    g *= 5**c5n
    p //= g
    n //= g
    m //= g
    
    # nには素因数としてn,mがない
    t = pow(-n,-1,p) * m % p
    print(t)
    return
t = II()
for i in range(t):
    solve(p)
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