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No.361 Kadomatsu Game 2

レベル : / AI推定難易度 : 1225 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 256 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 113
作問者 : koyumeishi / テスター : 🐬hec
お気に入りにしたユーザー ProblemId : 1016 / 自分の提出
問題文最終更新日: 2026-06-25 18:48:29
This statement was translated by AI (claude-opus-5-5, effort medium) and may contain errors or differ in nuance from the original. The original statement takes precedence. Back to the original
yukicoder 門松コンテスト (順位表) の他の問題:

Problem Statement

kado and matsu play a game in which they split bamboo to make kadomatsu.
The game proceeds as follows.
  • Initially, there is one piece of bamboo of length $L$ on the field.
  • The player whose turn it is chooses one piece of bamboo from the field and splits it into three pieces so that a kadomatsu can be made. The chosen piece is removed from the field, and the three pieces resulting from the split are added to the field.
    Here, letting $L$ be the length of the bamboo before the split and $L_1,L_2,L_3$ be the lengths of the pieces after the split, all of the following must be satisfied:
    • $L_1+L_2+L_3=L$
    • $L_1 \neq L_2, L_2 \neq L_3, L_3 \neq L_1$
    • $L_1,L_2,L_3$ are positive integers
    • $max(L_1,L_2,L_3)-min(L_1,L_2,L_3) \leq D$

    After splitting, the turn passes to the other player. If the player whose turn it is cannot split any bamboo so as to satisfy the conditions, that player loses.
  • The player who did not lose wins.
kado moves first and matsu moves second.
If both play optimally, who will win?

Input

L D

$L,D$ are integers satisfying the following.
$1 \leq D \leq L \leq 500$

Output

Print the name of the player who will win.

Sample

Sample 1
Input
7 3
Output
kado

If kado splits {7} -> {1,2,4}, the second player matsu cannot do anything and loses.

Sample 2
Input
7 2
Output
matsu

No split satisfying the conditions is possible from the start. {7} -> {1,2,4} is not allowed because max(1,2,4) - min(1,2,4) = 3 > D = 2.

Sample 3
Input
13 13
Output
matsu

The first player, kado, chooses one of the following ways to split:
{13} -> {1,2,10},{1,3,9},{1,4,8},{1,5,7},{2,3,8},{2,4,7},{2,5,6},{3,4,6}
and performs that split.
Bamboo of lengths 1 to 5 cannot be split any further so as to satisfy the conditions, so the second player, matsu, must split the longest piece.

  • {6} -> {1,2,3}
  • {7} -> {1,2,4}
  • {8} -> {1,2,5},{1,3,4}
  • {9} -> {1,2,6},{1,3,5},{2,3,4}
  • {10} -> {1,2,7},{1,3,6},{1,4,5},{2,3,5}
By choosing any split from {6}, {7}, or {8}, {1,3,5} or {2,3,4} from {9}, or {1,4,5} or {2,3,5} from {10}, matsu leaves kado with no bamboo that can be split on his next turn, so matsu wins.






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