## 5D Chests

Statement

## Goal

Pirx the Pilot is flying his spaceship through hyperspace in search of gold. Given a 5D realm with all dimensions ranging from 1 to N, each location (x,y,z,w,v) is either a chest of gold (1) or a barrier (0) as determined by the function:f(x,y,z,w,v)=isprime(1+ mod(x*y*z*w*v,C))

The barriers form rooms in hyperspace (Pirx can only move along the five dimensions, no diagonals). Help Pirx search every room and find all the gold.

Input

**First line:**The size

`N`of each dimension.

**Second line:**The constant

`C`for terrain generation.

Output

**First line:**The total number of gold chests.

**Second line:**The number of rooms that contain at least one chest.

**Third line:**The largest number of gold chests in one room.

Constraints

3 ≤

2 ≤

`N`≤ 202 ≤

`C`≤ 10,000Example

Input

5 8

Output

1141 236 216

Tags

Flood fill

Difficulty

Medium

Test cases

N=5 Test

Input

5
8

Output

1141
236
216

N=5 Validator

Input

5
23

Output

1382
74
651

N=10 Test

Input

10
77

Output

29552
3064
9090

N=10 Validator

Input

10
7777

Output

32251
3562
23325

N=15 Test

Input

15
11

Output

268939
1611
49408

N=15 Validator

Input

15
1111

Output

145380
38105
22030

N=20 Test

Input

20
9

Output

653072
143339
271

N=20 Validator

Input

20
99

Output

891383
137353
182225

Solution language

Solution

Stub generator input

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