Petya and Pipes

题意翻译

有一个 $n$ 个点的图 输入一个矩阵 $c$ 其中如果 $c_{ij}\neq 0$ ，表示 $i$ 到 $j$ 有一条容量为 $c_{ij}$ 的边, $c_{ii}$ 总是 $=0$ 你有 $k$ 元钱，每花 $1$ 元钱可以使得一条边已有容量 $+1$ $($ 你不能新建边 $)$ 问从 $1$ 到 $n$ 最大流量是多少

题目描述

A little boy Petya dreams of growing up and becoming the Head Berland Plumber. He is thinking of the problems he will have to solve in the future. Unfortunately, Petya is too inexperienced, so you are about to solve one of such problems for Petya, the one he's the most interested in. The Berland capital has $ n $ water tanks numbered from $ 1 $ to $ n $ . These tanks are connected by unidirectional pipes in some manner. Any pair of water tanks is connected by at most one pipe in each direction. Each pipe has a strictly positive integer width. Width determines the number of liters of water per a unit of time this pipe can transport. The water goes to the city from the main water tank (its number is $ 1 $ ). The water must go through some pipe path and get to the sewer tank with cleaning system (its number is $ n $ ). Petya wants to increase the width of some subset of pipes by at most $ k $ units in total so that the width of each pipe remains integer. Help him determine the maximum amount of water that can be transmitted per a unit of time from the main tank to the sewer tank after such operation is completed.

输入输出格式

输入格式

The first line contains two space-separated integers $ n $ and $ k $ ( $ 2<=n<=50 $ , $ 0<=k<=1000 $ ). Then follow $ n $ lines, each line contains $ n $ integers separated by single spaces. The $ i+1 $ -th row and $ j $ -th column contain number $ c_{ij} $ — the width of the pipe that goes from tank $ i $ to tank $ j $ ( $ 0<=c_{ij}<=10^{6},c_{ii}=0 $ ). If $ c_{ij}=0 $ , then there is no pipe from tank $ i $ to tank $ j $ .

输出格式

Print a single integer — the maximum amount of water that can be transmitted from the main tank to the sewer tank per a unit of time.

输入输出样例

输入样例 #1

5 7
0 1 0 2 0
0 0 4 10 0
0 0 0 0 5
0 0 0 0 10
0 0 0 0 0

输出样例 #1

10

输入样例 #2

5 10
0 1 0 0 0
0 0 2 0 0
0 0 0 3 0
0 0 0 0 4
100 0 0 0 0

输出样例 #2

5

说明

In the first test Petya can increase width of the pipe that goes from the $ 1 $ st to the $ 2 $ nd water tank by $ 7 $ units. In the second test Petya can increase width of the pipe that goes from the $ 1 $ st to the $ 2 $ nd water tank by $ 4 $ units, from the $ 2 $ nd to the $ 3 $ rd water tank by $ 3 $ units, from the $ 3 $ rd to the $ 4 $ th water tank by $ 2 $ units and from the $ 4 $ th to $ 5 $ th water tank by $ 1 $ unit.