401463: GYM100460 I Magic and Sword

It's time of the final battle! At the night of Superposition Desmond and Thorwald are fighting with evil Deimos in the throne room. Deimos is a powerful magician. He reads all kinds of attacking spells one after another, casting the i-th spell at the moment of time t_i. At this moment one of the heroes must start to take actions against the Deimos' spell, and it takes some time. If Desmond takes actions against the Deimos' spell, he will be fully concentrated on this operation for the next a_i seconds, and if Thorwald does it, he will require b_i seconds. If no hero takes action against the spell — consequences will be sorrowful: both of them will be eliminated, and Deimos will celebrate the victory.

All this becomes more complicated because the night of Superposition has already come and the fateful moment when it will be possible to start the ritual of opening the portal between worlds is very close. Deimos has already raised his dagger over princess Alatiel and is nervously glancing at the clock waiting for this. It means that not so far the gates to Xentaron — the native frozen world of Deimos — will be opened. In that world the powers of evil are already waiting for the gates being opened and fantasize what will they do with the remaining elves in Enia.

Desmond and Thorwald don't know how much time they have now. Our heroes have no illusions about their fighting qualities againts dark legions and about desires of Alatiel to take part in this ritual, so they would like to destroy the El-Gilet Sphere, without which the ritual cannot be held, as soon as possible. It should be done by Thorwald because in his hands there is the only thing that can break the Sphere — the Scepter of the First Kings of Enia. Breaking ancient elven artifacts is definitely easier than creating them, but even for this Thorwald requires c successive seconds, during which he cannot take part in the defense against the Deimos' spells. Desmond reads Deimos' tactic like an opened book, so he knows in advance all information about his spells and moments of their usage. Now Desmond wants to know how soon his comrade can destroy the Sphere. Desmond understands that just the Sphere is destroyed, Deimos will immediately interrupt the battle and surrender, even if just at this moment he is going to cast a spell.

The first line contains two integers separated by the space: n and c (1 ≤ n ≤ 10⁵, 1 ≤ c ≤ 10⁹) — the number of Deimos' spells and the time required to destroy the Sphere.

The second line contains n integers separated by the spaces: t_i (0 ≤ t_i ≤ t_i + 1 ≤ 10⁹) — the moments of time when Deimos casts his spells.

The third line contains n integers separated by the spaces: a_i (1 ≤ a_i ≤ 10⁹) — the time required by Desmond to act against the corresponding Deimos' spells.

The fourth line analogically contains n integers separated by the spaces: b_i (1 ≤ b_i ≤ 10⁹) — the time required by Thorwald to act against the corresponding Deimos' spells.

In the first line output «Radiant victory» (without quotes), if the heroes can survive from the Deimos' spells till the destroying of the El-Gilet Sphere. In this case in the second line output one integer — the minimal moment of time when the Sphere can be destroyed. And if the heroes are not destined to win this battle, output in the first line «Dire victory» (without quotes).

3 5
0 0 0
1 1 1
1 1 1

Dire victory

3 5
0 0 1
1 1 1
1 1 1

Radiant victory
6

3 5
5 5 5
1 1 1
1 1 1

Radiant victory
5