import sys
import time
import random
import math
import heapq
from collections import defaultdict

random.seed(42)

INF = 10**18

alpha = 5
alpha2 = alpha * alpha

def eprint(*args, **kwargs):
    print(*args, file=sys.stderr, **kwargs)

class TimeKeeper:
    """
    時間を管理するクラス
    時間制限を秒単位で指定してインスタンスをつくる
    """
 
    def __init__(self, time_threshold) -> None:
        self.start_time_ = time.time()
        self.time_threshold_ = time_threshold
 
    def isTimeOver(self) -> bool:
        """
        インスタンスを生成した時から指定した時間制限を超過したか判断する  
        超過している場合にTrue  
        """
        return time.time() - self.start_time_ - self.time_threshold_ >= 0
 
    def time_msec(self) -> int:
        """経過時間をミリ秒単位で返す"""
        return int((time.time() - self.start_time_) * 1000)

    def time_sec(self) -> int:
        """経過時間を秒単位で返す(time_msecの使用を推奨)"""
        return time.time()-self.start_time_

class Kmeans:
    
    def __init__(self, X:list, n_data:int, k:int):
        self.x = [[t.x, t.y] for t in X]
        self.n_data = n_data
        self.k = k

    def init_centroid(self):
        idx = random.sample(range(self.n_data), self.k)
        centroids = [self.x[i] for i in idx]
        return centroids
    
    def compute_distance(self, centroids):
        distances = []
        for x in self.x:
            dist = [math.sqrt(sum([(a - b) ** 2 for a, b in zip(x, centroid)])) for centroid in centroids]
            distances.append(dist)
        return distances
    
    def clustering(self):
        centroids = self.init_centroid()
        new_cluster = [0]*self.n_data
        cluster = [0]*self.n_data
        for epoch in range(100):
            distances = self.compute_distance(centroids)
            new_cluster = [min(range(len(d)), key=lambda i: d[i]) for d in distances]
            for idx_centroid in range(self.k):
                x_in_cluster = [self.x[i] for i in range(self.n_data) if new_cluster[i] == idx_centroid]
                if x_in_cluster:
                    centroids[idx_centroid] = [int(sum(coord)/len(x_in_cluster)) for coord in zip(*x_in_cluster)]
            if new_cluster == cluster:
                break
        #cluster = new_cluster
        return centroids


class Input:
    def __init__(self, N:int, M:int, ab:list) -> None:
        self.N = N
        self.M = M
        self.ab = ab

class Parser:

    def __init__(self, input_type:int):
        self.flag = input_type

    def parse(self):
        if self.flag == -1:
            inp:Input = self.parse_input()
        else:
            inp:Input = self.parse_input_file(self.flag)
        return inp
    
    def parse_input(self) -> Input:
        N,M = map(int,input().split())
        ab = [list(map(int,input().split())) for i in range(N)]
        return Input(N,M,ab)


    def parse_input_file(self,num) -> Input:
        cnt = str(num).zfill(4)
        PATH = f"./in/{cnt}.txt"
        with open(PATH) as f:
            l = [s.strip() for s in f.readlines()]
            N, M = map(int,l[0].split())
            ab = [list(map(int,s.split())) for s in l[1:]]
            return Input(N, M, ab)

class Transit:

    def __init__(self, id:int, x:int, y:int, type:int) -> None:
        """
        id:int id of planet or station
        x:int x coordinate
        y:int y coordinate
        type:int 1 planet, 2 station
        """
        self.id = id
        self.x = x
        self.y = y
        self.type = type
        self.key = self.type * 1000 + self.id

    def __lt__(self, other) -> bool:
        return self.key < other.key
    
    def __eq__(self, other) -> bool:
        return self.key == other.key
    
    def __str__(self) -> str:
        return f"({self.id},{self.x},{self.y},{self.type})"

class State:
    
    def __init__(self, order:list, planets:list, stations:list, dist_mat:list) -> None:
        """
        order:list visited order 
        stations:list[(int,int)] coordinates of space station
        """
        self.order = order
        self.planets = planets
        self.stations = stations
        self.links = self.prepare_edges()
        self.dist_mat = dist_mat
    
    def prepare_edges(self):
        """
        edges:dictを返す
        edges[Transit_from_key:int] = [(dist, Transit_to), ...]
        """
        edges = defaultdict(list)
        for planet_from in self.planets:
            for planet_to in self.planets: # planet to planet
                if planet_from == planet_to: continue
                edges[planet_from.key].append((self.cal_dist(planet_from, planet_to), planet_to))
            for station_to in self.stations: # planet to station
                edges[planet_from.key].append((self.cal_dist(planet_from, station_to), station_to))
        for station_from in self.stations: # station to station
            for planet_to in self.planets:
                edges[station_from.key].append((self.cal_dist(station_from, planet_to), planet_to))
            for station_to in self.stations:
                if station_from == station_to: continue
                edges[station_from.key].append((self.cal_dist(station_from, station_to), station_to))
        return edges

    
    def cal_dist(self, v1:Transit, v2:Transit) -> float:
        """
        return distance between v1 and v2 weighted by coefficient
        """
        x1,y1 = v1.x, v1.y
        x2,y2 = v2.x, v2.y
        coef = alpha
        if v1.type == 1 and v2.type == 1: coef = alpha2 # planet to planet
        elif v1.type == 2 and v2.type == 2: coef = 1 # station to station
        d = ((x1-x2)**2+(y1-y2)**2) * coef
        return d
    
    def cal_score(self):
        score = 0
        for i in range(len(self.order)-1):
            score += self.cal_dist(self.order[i], self.order[i+1])
        return int(pow(10,9)/(1000+score**0.5))

def trace(start:Transit, target:Transit, ancestors): 
    # s:source, t:target
    # dijksttra法の経路復元
    route = [target]
    now = target
    while True:
        pre = ancestors[now.key]
        route.append(pre)
        if pre == start:
            break
        now = pre
    route.reverse()
    return route

def dijkstra(start:Transit, target:Transit, links):
    heap = [(*l,start) for l in links[start.key]]
    heapq.heapify(heap)
    visited = set([start.key])
    ancestors = defaultdict(int)
    while heap:
        cost, to, ancestor = heapq.heappop(heap)
        if to.key in visited:
            continue
        visited.add(to.key)
        ancestors[to.key] = ancestor
        if to == target:
            return cost, trace(start,target,ancestors)
        for cost2, node2 in links[to.key]:
            if node2.key not in visited:
                heapq.heappush(heap, (cost+cost2, node2, to))
    return INF, None

def warshall_floyd(planets:list):
    n = len(planets)
    dist = [[INF]*n for _ in range(n)]
    for i in range(n):
        dist[i][i] = 0
    for i in range(n):
        for j in range(i+1,n):
            d = (planets[i].x - planets[j].x) ** 2 + (planets[i].y - planets[j].y) ** 2
            dist[i][j] = d
            dist[j][i] = d
    for k in range(n):
        for i in range(n):
            for j in range(n):
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])
    return dist


class Output:
    
    def __init__(self, state:State) -> None:
        self.order = state.order
        self.stations = state.stations

    def ans(self):
        for transition in self.stations:
            print(transition.x, transition.y)
        print(len(self.order))
        for transition in self.order:
            print(transition.type, transition.id+1)

class Solver:
    def __init__(self, state:State) -> None:
        self.state = state
    
    def solve(self):
        
        self.state.order.append(self.state.planets[0])
        visited = [0]*len(self.state.planets)
        visited[0] = 1
        now = self.state.planets[0]
        next = Transit(-1,-1,-1,-1)
        n_visited = set([0])
        
        while len(n_visited) < len(self.state.planets):
            next_dist = []
            for i in range(len(self.state.planets)):
                next_dist.append((self.state.dist_mat[now.id][i], i))
            next_dist = sorted(next_dist, key=lambda x:x[0])
            for i in range(len(self.state.planets)):
                if visited[next_dist[i][1]] == 1: continue
                next = self.state.planets[next_dist[i][1]]
                break
            _, route = dijkstra(now, next, self.state.links)
            for transition in route:
                self.state.order.append(transition)
            now = next
            visited[next.id] = 1
            n_visited.add(next.id)

        _, route = dijkstra(now, self.state.planets[0], self.state.links)
        for transition in route:
            self.state.order.append(transition)
    
        return self.state

def main():

    timeKeeper2 = TimeKeeper(0.83)

    parser = Parser(-1)
    input = parser.parse()
    
    planets = []
    for i in range(input.N):
        planets.append(Transit(id = i, x = input.ab[i][0], y = input.ab[i][1], type = 1))
    dist_mat = warshall_floyd(planets)

    kmeans_center = Kmeans(planets, 100, 8).clustering()
    stations = []
    for i in range(input.M):
        stations.append(Transit(id = i,x = kmeans_center[i][0],y = kmeans_center[i][1],type = 2))
    
    state = State([], planets, stations, dist_mat)
    solver = Solver(state)
    best_ans = solver.solve()
    best_score = best_ans.cal_score()
    #eprint(timeKeeper2.time_msec(), best_score)

    tmp_stations = best_ans.stations
    
    while not timeKeeper2.isTimeOver():
        order = []
        stations = []
        for i in range(input.M):
            x_new = 0
            y_new = 0
            while True:
                x_new = tmp_stations[i].x+random.randrange(-20,20)
                y_new = tmp_stations[i].y+random.randrange(-20,20)
                if x_new >= 0 and x_new <= 1000 and y_new >= 0 and y_new <= 1000:
                    break
            stations.append(Transit(id = i,x = x_new, y = y_new, type = 2))
        state = State(order,planets,stations, dist_mat)
        solver = Solver(state)
        ans = solver.solve()
        score = ans.cal_score()
        #eprint(timeKeeper2.time_msec(), score)
        if score > best_score:
            best_score = score
            best_ans = ans
            tmp_stations = stations
    eprint(best_score)
    output = Output(best_ans)
    output.ans()


if __name__ == "__main__":
    main()