Problem:
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You are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0, 1, ... n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$.

Write a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.

Input

In the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.

Output

Print the minimum value of $P$ in a line.

Constraints

$1 \leq n \leq 100,000$

$1 \leq k \leq 100,000$

$1 \leq w_i \leq 10,000$

Sample Input 1

5 3
8
1
7
3
9

Sample Output 1

10

If the first truck loads two packages of $\{8, 1\}$, the second truck loads two packages of $\{7, 3\}$ and the third truck loads a package of $\{9\}$, then the minimum value of the maximum load $P$ shall be 10.

Sample Input 2

4 2
1
2
2
6

Sample Output 2

6

If the first truck loads three packages of $\{1, 2, 2\}$ and the second truck loads a package of $\{6\}$, then the minimum value of the maximum load $P$ shall be 6.

Solution in JAVA (judge verdict: Accepted)

import java.io.*;
import java.math.*;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
import java.lang.ArrayIndexOutOfBoundsException;

/**
 * @author yoshikyoto
 */
class Main extends MyUtil{
	// public static ArrayList<ArrayList<Integer>> g;
	public static Graph g;
	
	static int n, k, w[];
	public static void main(String[] args) throws Exception{
		n = sc.nextInt();
		k = sc.nextInt();
		
		w = new int[n];
		int max = 0, min = 0;
		for (int i = 0; i < n; i++) {
			w[i] = sc.nextInt();
			max += w[i];
			min = Math.max(min, w[i]);
		}
		System.out.println(dfs(1, 1000000000));
	}
	
	static int dfs(int min, int max){
		if(min == max) return min;
		int p = (min + max) / 2;
		// トラックの容量をcenterとしてやってみる
		// System.out.println("容量" + p + "とする");
		
		int sum = 0, count = 1;
		for (int i = 0; i < n; i++) {
			if(p < w[i]) return dfs(p+1, max);
			if(sum + w[i] > p) {
				sum = w[i];
				count++;
			}else{
				sum += w[i];
			}
		}
		
		// System.out.println("p: " + p + "\tcount: " + count);
		if(count <= k){
			// System.out.println("容量小さくできないか試みる");
			return dfs(min, p);
		}else{
			// System.out.println("容量を大きくしないといけない");
			return dfs(p+1, max);
		}
	}
}


class Data extends MyUtil{
	String name;
	int time, finishedAt;
	Data(String str){
		String[] strs = str.split(" ");
		name = strs[0];
		time = parseInt(strs[1]);
	}
}


class DataComparator implements Comparator<Data>{
    public int compare(Data a, Data b) {
    	return a.finishedAt - b.finishedAt;
    	// a-bで昇順
    	/*
        if (a.point != b.point) {
            return a.point - b.point;
        } else {
        	return a.name.compareTo(b.name);
        }
        */
    }
}

class ArrayComparator implements Comparator<int[]>{
	public int compare(int[] a, int[] b){
		int l = Math.min(a.length, b.length);
		for(int i = 0; i < l; i++){
			if(a[i] == b[i]) continue;
			return b[i] - a[i];
		}
		return 0;
	}
}

class Node extends ArrayList<Edge>{
	int index, depth = -1, dist = -1;
	Node(int index){this.index = index;}
	Node parent;
	boolean visited = false;
}
class Edge{
	int from, to, cost;
	Edge(int from, int to, int cost){
		this.from = from;
		this.to = to;
		this.cost = cost;
	}
}
class NodeComparator implements Comparator<Node>{
	public int compare(Node a, Node b){
		return a.dist - b.dist;
	}
}

class Graph{
	Node n[];
	Graph(int node_count){
		n = new Node[node_count];
		for(int i = 0; i < node_count; i++) n[i] = new Node(i);
	}
	public void add(Edge e){
		n[e.from].add(e);
	}
	public Node get(int i){return n[i];}
	public Node lca(int a, int b){
		// 浅い方をaとする
		Node nodeA, nodeB;
		if(n[a].depth < n[b].depth){
			nodeA = n[a];
			nodeB = n[b];
		}else{
			nodeA = n[b];
			nodeB = n[a];
		}
		// 同じ深さまで親をたどる
		int diff = nodeB.depth - nodeA.depth;
		for(int k = 0; k < diff; k++){
			nodeB = nodeB.parent;
		}
		// 共通祖先を見つける
		while(nodeA != nodeB){
			nodeA = nodeA.parent;
			nodeB = nodeB.parent;
		}
		return nodeA;
	}
	void calcDepth(int root){
		QI que = new QI();
		que.push(root);
		n[root].depth = 0;
		
		while(que.size() > 0){
			int curr = que.pop();
			Node curr_node = n[curr];
			for(Edge e : curr_node){
				int next = e.to;
				Node next_node = n[next];
				if(next_node.depth == -1){
					next_node.depth = curr_node.depth + 1;
					next_node.parent = curr_node;
					que.push(next);
				}
			}
		}
	}
	
	int[] dijkstra(int s){
		PriorityQueue<Node> q = new PriorityQueue<Node>(n.length, new NodeComparator());
		Node start_node = new Node(s);
		start_node.dist = 0;
		q.add(start_node);
		int[] dist = new int[n.length];
		for (int i = 0; i < dist.length; i++)  dist[i] = -1;
		dist[s] = 0;
		
		while(q.size() > 0){
			Node currNode = q.poll();
			// System.out.println(currNode.dist + " " + dist[currNode.index] + " " + currNode.dist);
			if(dist[currNode.index] < currNode.dist) continue;
			for(Edge e : n[currNode.index]){
				Node nextNode = new Node(e.to);
				nextNode.dist = currNode.dist + e.cost;
				if(dist[e.to] == -1 || dist[e.to] > nextNode.dist){
					dist[e.to] = nextNode.dist;
					q.add(nextNode);
				}
			}
		}
		return dist;
	}
}



class Regex{
	Pattern p; Matcher m; String str;
	Regex(String regex_str){p = Pattern.compile(regex_str);}
	void setStr(String str){m = p.matcher(str);}
	boolean find(){return m.find();}
	String group(int i){return m.group(i);}
	String group(){return m.group();}
}

/**
 * UnionFindTree Set周りは未実装
 * @author yoshikyoto
 */
class UnionFindTree{
    public int[] parent, rank;
    public int n;
    public Set<Integer> set;
    // 初期化
    UnionFindTree(int n){
        this.n = n;
        for(int i = 0; i < n; i++){
        	parent = new int[n];
        	rank = new int[n];
            parent[i] = i;
            rank[i] = 0;
        }
    }
    // 根を求める
    int find(int x){
        if(parent[x] == x){
            return x;
        }else{
            return parent[x] = find(parent[x]);
        }
    }
    // xとyの集合を結合
    void unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y){
            return;
        }
        if(rank[x] < rank[y]){
            parent[x] = y;
        }else{
            parent[y] = x;
            if(rank[x] == rank[y]) rank[x]++;
        }
    }
    // xとyが同じ集合か
    boolean same(int x, int y){
        return find(x) == find(y);
    }
};


/**
 * 整数を数え上げたりするクラス
 * new Prime(int n) でnまでエラトステネスの篩を実行。
 * @author yoshikyoto
 * @param a[i] iが素数の時true
 * @param count[i] i以下の素数の数
 */
class Prime{
	boolean[] a;
	int[] count;
	Prime(int n){
		a = new boolean[n+1];
		a[0] = false; a[1] = false;
		for(int i = 2; i <= n; i++) a[i] = true;
		// ふるい
		for(int i = 2; i < (n - 3) / 2; i++)
			if(a[i]) for(int j = 2; j * i <= n; j++)
					a[j * i] = false;
		
		// 数え上げ
		count = new int[n+1];
		count[0] = 0;
		for(int i = 1; i <= n; i++){
			int gain = 0;
			if(a[i]) gain = 1;
			count[i] = count[i-1] + gain;
		}
	}
	boolean isPrime(int i){return a[i];}
	static boolean calcPrime(int i){
		if(i <= 1) return false;
		if(i == 2) return true;
		if(i % 2 == 0) return false;
		for(int j = 3; j <= Math.sqrt(i); j+=2){
			if(i % j == 0) return false;
		}
		return true;
	}
}

class AI extends ArrayList<Integer>{}
class SI extends Stack<Integer>{}

class CountHashMap<E> extends HashMap<E, Integer>{
	ArrayList<E> keyArray = new ArrayList<E>();
	public void add(E key){add(key, 1);}
	public void add(E key, Integer value){
		if(containsKey(key)){value += get(key);
		}else{keyArray.add(key);}
		put(key, value);
	}
}
class HM extends CountHashMap<String>{} 

class Q<E> extends ArrayDeque<E>{
	public void push(E item){add(item);}
	public E pop(){return poll();}
}
class QS extends Q<String>{}
class QI extends Q<Integer>{}

/**
 * MyUtil
 * @author yoshikyoto
 */
class MyUtil extends MyIO{
	public static int[] vy={-1,1,0,0}, vx={0,0,-1,1};
	public static Random rand = new Random();
	public static int digit(int n){return String.valueOf(n).length();}
	public static String reverse(String s){
		return (new StringBuffer(s)).reverse().toString();
	}
	public static void dsort(int[] a){
		Arrays.sort(a);
		int l = a.length;
		for(int i = 0; i < l/2; i++){
			int tmp = a[i]; a[i] = a[l-1-i]; a[l-1-i] = tmp;
		}
	}
	public static void sleep(int t){try{Thread.sleep(t);}catch(Exception e){}}
	public static int sum(int[] a){int s = 0; for(int i = 0; i < a.length; i++)s+=a[i]; return s;}
	public static int[] cp(int[] a){
		int[] b = new int[a.length];
		for(int i = 0; i < a.length; i++) b[i] = a[i];
		return b;
	}
	public static int randomInt(int min, int max){return min + rand.nextInt(max - min + 1);}
	static boolean inside(int y, int x, int h, int w){return 0 <= y && y <= (h-1) && 0 <= x && x <= (w-1);};
	public static boolean isUpper(char c){return 'A'<=c&&c<='Z';}
	public static boolean isLower(char c){return 'a'<=c&&c<='z';}
	public static char toUpper(char c){
		if(isLower(c)) return (char)(c - 'a' + 'A');
		return c;
	}
	public static char toLower(char c){
		if(isUpper(c)) return (char)(c - 'A' + 'a');
		return c;
	}
	public static int[] swap(int[] arr, int i, int j){
		int[] ret = cp(arr);
		int tmp = ret[i];
		ret[i] = ret[j];
		ret[j] = tmp;
		return ret;
	}
}

/**
 * MyIO
 * @author yoshikyoto
 */
class MyIO extends MyMath{
	static Scanner sc = new Scanner(new InputStreamReader(System.in));
	public static char scNextChar(){return sc.next().charAt(0);}
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	public static String line;
	public static int[] readIntMap() throws IOException{return parseInt(readLine().split(" "));}
	public static int[] readIntMap(int n) throws IOException{
		int[] ret = new int[n];
		for(int i = 0; i < n; i++) ret[i] = readInt();
		return ret;
	}
	public static int[] readNoDistIntMap() throws IOException{
		String[] strs = readLine().split("");
		int l = strs.length;
		int[] ret = new int[l-1];
		for(int i = 1; i < l; i++)
			ret[i-1] = parseInt(strs[i]);
		return ret;
	}
	public static boolean readToLine() throws IOException{return (line = br.readLine()) != null;}
	public static String readLine() throws IOException{return br.readLine();}
	public static int readInt() throws IOException{return Integer.parseInt(br.readLine());}
	public static int[] parseInt(String[] arr){
		int[] res = new int[arr.length];
		for(int i = 0; i < arr.length; i++)res[i] = Integer.parseInt(arr[i]);
		return res;
	}
	public static double[] parseDouble(String[] arr){
		double[] res = new double[arr.length];
		for(int i = 0; i < arr.length; i++)res[i] = Double.parseDouble(arr[i]);
		return res;
	}
	public static boolean[] parseBool(String[] arr){
		int[] t = parseInt(arr);
		boolean[] res = new boolean[t.length];
		for(int i = 0; i < t.length; i++){
			if(t[i] == 1){res[i] = true;
			}else{res[i] = false;}
		}
		return res;
	}
	public static int parseInt(Object o){return Integer.parseInt(o.toString());}
}

class MyMath{
	/**
	 * 弧度法の角度を入力してsinの値を返す（Math.sin の入力はラジアン）
	 */
	public static double sin(int r){return Math.sin(Math.toRadians(r));}

	/**
	 * 弧度法の角度を入力してcosの値を返す（Math.sin の入力はラジアン）
	 */
	public static double cos(int r){return Math.cos(Math.toRadians(r));}
	public static int max(int[] arr){return max(arr, 0, arr.length-1);}
	public static int max(int[] arr, int l, int r){
		int max = arr[l];
		for(int i = l+1; i <= r; i++)
			max = Math.max(max, arr[i]);
		return max;
	}
	public static int min(int[] arr){return min(arr, 0, arr.length-1);}
	public static int min(int[] arr, int l, int r){
		int min = arr[l];
		for(int i = l+1; i <= r; i++)
			min = Math.min(min, arr[i]);
		return min;
	}
	public static boolean isCross(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4){
	    // 並行な場合
	    int m = (x2-x1)*(y4-y3)-(y2-y1)*(x4-x3);
	    if(m == 0) return false;
	    // 媒介変数の値が0より大きく1以下なら交差する、これは問題の状況によって変わるかも。
	    double r =(double)((y4-y3)*(x3-x1)-(x4-x3)*(y3-y1))/m;
	    double s =(double)((y2-y1)*(x3-x1)-(x2-x1)*(y3-y1))/m;
	    return (0 < r && r <= 1 && 0 < s && s <= 1);
	}
	public static boolean isParallel(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4){
	    if((x2-x1)*(y4-y3) == (y2-y1)*(x4-x3)) return true;
	    else return false;
	}
	public static double sq(double d){return d*d;}
	public static int sq(int i){return i*i;}
	public static int sqdist(int x1, int y1, int x2, int y2){
		return (x1-x2) + sq(y1-y2);}
	public static double sqdist(double x1, double y1, double x2, double y2){
		return sq(x1-x2) + sq(y1-y2);}
	public static double dist(int x1, int y1, int x2, int y2){
		return Math.sqrt(sqdist(x1, y1, x2, y2));}
	public static double dist(double x1, double y1, double x2, double y2){
		return Math.sqrt(sqdist(x1, y1, x2, y2));}
	long comb(long n, long m){
		if(n < m) return 0;
    	long c = 1; m = (n - m < m ? n - m : m);
    	for(long ns = n - m + 1, ms = 1; ms <= m; ns ++, ms ++){c *= ns; c /= ms;}
    	return c;
    }
	static int gcd(int a, int b){if(a%b==0){return(b);}else{return(gcd(b,a%b));}};
	/**
	 * aの中から、合計がborderを超えるペア（重複除く）の数を数える
	 */
	static int countPair(int[] a, int border){
		int count = 0, l = a.length, i = 0, j = l-1;
		for (; i < l; i++) {
			for (; j >= 0; j--) if(a[i] + a[j] <= border) break;
			count += l - (j + 1);
			if(j < i) count--;
		}
		return count/2;
	}
}