Product Development

AtCoder

IDabc322_e

Time4000ms

Memory256MB

Difficulty—

AtCoder Inc. is planning to develop a product. The product has $K$ parameters, whose values are currently all zero. The company aims to raise all parameter values to at least $P$. There are $N$ development plans. Executing the $i$\-th development plan ($1 \le i \le N$) increases the value of the $j$\-th parameter by $A_{i,j}$ for every integer $j$ such that $1 \le j \le K$, at the cost of $C_i$. A development plan cannot be executed more than once. Determine whether the company can achieve its goal, and if it can, find the minimum total cost required to achieve the goal. ## Constraints * $1 \le N \le 100$ * $1 \le K,P \le 5$ * $0 \le A_{i,j} \le P(1 \le i \le N,1 \le j \le K)$ * $1 \le C_i \le 10^9(1 \le i \le N)$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $P$ $C_1$ $A_{1,1}$ $A_{1,2}$ $\dots$ $A_{1,K}$ $C_2$ $A_{2,1}$ $A_{2,2}$ $\dots$ $A_{2,K}$ $\dots$ $C_N$ $A_{N,1}$ $A_{N,2}$ $\dots$ $A_{N,K}$ [samples]

Samples

Input #1

Output #1

9

If you execute the first, third, and fourth development plans, each parameter will be $3+2+0=5,0+4+1=5,2+0+4=6$, all of which are at least $5$, so the goal is achieved. The total cost in this case is $5 + 3 + 1 = 9$.
It is impossible to achieve the goal at a total cost of $8$ or less. Thus, the answer is $9$.

Input #2

Output #2

\-1

You cannot achieve the goal no matter what you do. Thus, print `-1`.

API Response (JSON)

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    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "abc322_e"
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      "statement_type": "Markdown",
      "content": "AtCoder Inc. is planning to develop a product. The product has $K$ parameters, whose values are currently all zero. The company aims to raise all parameter values to at least $P$.\nThere are $N$ develo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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