Z mod X = C (Codeforces 1684B)
Tags: Math, constructive algorithms

You are given three positive integers $$$a$$$, $$$b$$$, $$$c$$$ ($$$a < b < c$$$). You have to find three positive integers $$$x$$$, $$$y$$$, $$$z$$$ such that:$$$$$$x \bmod y = a,$$$$$$ $$$$$$y \bmod z = b,$$$$$$ $$$$$$z \bmod x = c.$$$$$$Here $$$p \bmod q$$$ denotes the remainder from dividing $$$p$$$ by $$$q$$$. It is possible to show that for such constraints the answer always exists.

Input: The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10\,000$$$) — the number of test cases. Description of the test cases follows.Each test case contains a single line with three integers $$$a$$$, $$$b$$$, $$$c$$$ ($$$1 \le a < b < c \le 10^8$$$).

Output: For each test case output three positive integers $$$x$$$, $$$y$$$, $$$z$$$ ($$$1 \le x, y, z \le 10^{18}$$$) such that $$$x \bmod y = a$$$, $$$y \bmod z = b$$$, $$$z \bmod x = c$$$.You can output any correct answer.

Note: In the first test case:$$$$$$x \bmod y = 12 \bmod 11 = 1;$$$$$$$$$$$$y \bmod z = 11 \bmod 4 = 3;$$$$$$$$$$$$z \bmod x = 4 \bmod 12 = 4.$$$$$$

Sample Inputs:
4
1 3 4
127 234 421
2 7 8
59 94 388

Sample Outputs:
12 11 4
1063 234 1484
25 23 8
2221 94 2609

Solution (Python):
import sys
input = sys.stdin.buffer.readline
ii = lambda : int(input())
si = lambda : input()
mi = lambda : map(int, input().split())
mf = lambda : map(float, input().split())
msi = lambda : map(str, input().strip().split(' '))
li = lambda : list(mi())
lf = lambda : list(mf())

def YES():
    sys.stdout.write('YES\n')

def Yes():
    sys.stdout.write('Yes\n')

def yes():
    sys.stdout.write('yes\n')

def NO():
    sys.stdout.write('NO\n')

def No():
    sys.stdout.write('No\n')

def no():
    sys.stdout.write('no\n')

class Solution:

    def __init__(self):
        return

    def solve(self):
        for _ in range(ii()):
            (a, b, c) = mi()
            sys.stdout.write(f'{a + b + c} {b + c} {c}\n')
if __name__ == '__main__':
    Solution().solve()

Solution (Python):
for s in [*open(0)][1:]:
    (a, b, c) = map(int, s.split())
    print(a + b * c, b, c)

Solution (Python):
def bata_na_lavde(a, b, c):
    l = c
    m = b + l
    f = a + m
    lst = [f, m, l]
    lst = [str(e) for e in lst]
    return ' '.join(lst)
t = int(input())
res = []
for i in range(t):
    (a, b, c) = map(int, input().split())
    res.append(bata_na_lavde(a, b, c))
for e in res:
    print(e)