Overview

This problem asks you to divide the number of sweets of each type \(A_i\) by the number of people \(M\), and for all types \(i=1..N\), compute and output the “number of sweets each person receives (quotient)” and the “remainder.”

Analysis

Since each type of sweet is “distributed equally to everyone,” the result of dividing \(A_i\) equally among \(M\) people directly gives the answer. In other words, the pair \((Q_i, R_i)\) satisfying \(A_i = M \times Q_i + R_i\) (where \(0 \le R_i < M\)) is simply the quotient and remainder of division.

For example, when \(M=4, A_i=14\): - Each person receives \(Q_i = 3\) sweets (\(3 \times 4 = 12\) sweets distributed) - The remainder is \(R_i = 2\) sweets (\(14-12=2\))

A naive simulation such as “subtract one at a time for the distributable amount” would be extremely slow for even a single type since \(A_i\) can be up to \(10^9\), resulting in TLE. However, since the quotient and remainder can be obtained in a single division operation, each \(A_i\) can be processed in \(O(1)\).

Algorithm

1. Read \(N, M\) and the array \(A\) from input.
2. For each \(a \in A\):
   • Compute \((q, r) = (a // M, a \bmod M)\) (in Python, divmod(a, M) is convenient).
3. Output q r on each line.

Complexity

• Time complexity: \(O(N)\) (one division per \(A_i\))
• Space complexity: \(O(N)\) (if accumulating output to print all at once at the end)

Implementation Notes

• In Python, using divmod(a, M) obtains both the quotient and remainder simultaneously, making the implementation concise.

• Since \(N\) can be up to \(2 \times 10^5\), using sys.stdin.buffer.read() and "\n".join(...) to handle input/output in bulk is faster.

  Source Code

import sys

def main():
    data = list(map(int, sys.stdin.buffer.read().split()))
    if not data:
        return
    N, M = data[0], data[1]
    A = data[2:2+N]
    out = []
    for a in A:
        q, r = divmod(a, M)
        out.append(f"{q} {r}")
    sys.stdout.write("\n".join(out))

if __name__ == "__main__":
    main()

This editorial was generated by gpt-5.2-high.