Problem:
Score : 300 points

Problem

Takahashi, who is a novice in competitive programming, wants to learn M algorithms.
Initially, his understanding level of each of the M algorithms is 0.

Takahashi is visiting a bookstore, where he finds N books on algorithms.
The i-th book (1\leq i\leq N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i,j} for each j (1\leq j\leq M).
There is no other way to increase the understanding levels of the algorithms.

Takahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.

Constraints

All values in input are integers.

1\leq N, M\leq 12

1\leq X\leq 10^5

1\leq C_i \leq 10^5

0\leq A_{i, j} \leq 10^5

Input

Input is given from Standard Input in the following format:

N M X
C_1 A_{1,1} A_{1,2} \cdots A_{1,M}
C_2 A_{2,1} A_{2,2} \cdots A_{2,M}
\vdots
C_N A_{N,1} A_{N,2} \cdots A_{N,M}

Output

If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.

Sample Input 1

3 3 10
60 2 2 4
70 8 7 9
50 2 3 9

Sample Output 1

120

Buying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.

Sample Input 2

3 3 10
100 3 1 4
100 1 5 9
100 2 6 5

Sample Output 2

-1

Buying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.

Sample Input 3

8 5 22
100 3 7 5 3 1
164 4 5 2 7 8
334 7 2 7 2 9
234 4 7 2 8 2
541 5 4 3 3 6
235 4 8 6 9 7
394 3 6 1 6 2
872 8 4 3 7 2

Sample Output 3

1067

Solution in Julia (1.4.0) (judge verdict: Accepted)

import Base.parse
import Base.StringVector

parse(::Type{String},  str::AbstractString) = str

isdelim(x::UInt8, xs::Set{UInt8}) = x in xs

function myreaduntil(s::IO, delims::Set{UInt8})::Vector{UInt8}
    out = StringVector(0)
    c::UInt8 = 0x00
    while !eof(s)
        c = read(s, UInt8)
        if !isdelim(c, delims)
            break
        end
    end
    push!(out, c)
    if eof(s)
        return out
    end
    while !eof(s)
        c = read(s, UInt8)
        if isdelim(c, delims)
            break
        end
        push!(out, c)
    end
    return out
end

delimset = Set([0x0a, 0x20])

function readword(io::IO = stdin, delims = delimset)::String
    word = myreaduntil(io, delims)
    i = length(word)
    if i == 0 || word[i] != 0x0a
        return String(word)
    elseif i < 2 || word[i-1] != 0x0d
        return String(resize!(word,i-1))
    else
        return String(resize!(word,i-2))
    end
end

pread(ty) = parse(ty, readword())

reads(tys...)::Tuple{tys...} = Tuple{tys...}(pread(ty) for ty in tys)

readvec(tys::Tuple , len::Signed)::Vector{Tuple{tys...}} = @inbounds Tuple{tys...}[reads(tys...) for i in 1:len]

readvec(ty::Type, len::Signed)::Vector{ty} = @inbounds ty[pread(ty) for i in 1:len]

function readmat(ty::Type, s...)::Matrix{ty}
    v = Matrix{ty}(undef, s...)
    @inbounds for i = 1:s[1]
        v[i,:] = readvec(ty, s[2])
    end
    v
end

function ds(c, a, val, cost, checked, x, l=0, s=length(c))
    if l == s
        return (sum(map(y -> y >= x, val)) == length(val), checked, cost)
    end
    bc = typemax(Int)
    br = nothing
    tmp = ds(c, a, val, cost, checked, x, l+1)
    if tmp[1]
        if bc > tmp[3]
            bc = tmp[3]
            br = tmp
        end
    end
    checked[l+1] = true
    val += a[l+1,:]
    cost += c[l+1]
    tmp = ds(c, a, val, cost, checked, x, l+1)
    if tmp[1]
        if bc > tmp[3]
            bc = tmp[3]
            br = tmp
        end
    end
    checked[l+1] = false
    if isnothing(br)
        return (false, checked, bc)
    else
        return br
    end
end

function main()
    N,M,X = reads(Int,Int,Int)
    c = zeros(Int, N)
    a = zeros(Int, N,M)
    for i in 1:N
        c[i] = pread(Int)
        a[i,:] = readvec(Int, M)
    end
    ans = ds(c, a, zeros(Int, M), 0, zeros(Int, N), X)
    if !ans[1]
        println(-1)
    else
        println(ans[3])
    end
end

main()