[left|overline{A_1} igcap overline{A_2} igcap cdots igcap overline{A_n}
ight| = left|S
ight|-sum_ileft|A_i
ight|+sum_{i<j}left| A_i igcap A_j
ight|- sum_{i<j<k}left|A_i igcap A_j igcap A_k
ight| + cdots+ (-1)^nleft|A_1 igcap A_2 igcap cdots igcap A_n
ight|
]
[S_k=C(n,k)*(2^{2^{n-k}}-1)
]
[sum_{j=k}^n(-1)^{j-k}S_j
]
[2^{2^t}=2^{2^{t-1}}*2^{2^{t-1}}
]
[f[i][j][k] = sum f[i-1][j-x][k-y]*g[i][x][y]*{n-j+x choose x}*{m-k+y choose y } (1 leq x < j land 1leq y < k land cnt[i] leq x*y)
]
[g[i][j][k]=sum(-1)^{a+b} {(j-a)*(k-b) choose cnt[i]} (1leq a < j land 1 leq b < k land cnt[i] leq (j-a)*(k-b) )
]
[ans=(-1)^{x+y+z} f[i-x][j-y][k-z]*{i choose x}*{j choose y}*{k choose z}
]
[f[i][j][k]=(k+1)^{i*j}
]
[left{ egin{array} {c} k*A_x+j*B_x=Ex \ k*A_y+j*B_y=Ey end{array}
ight.
]
[{j+k choose k}
]
[f[i]=g[0][i]-sum_{j=1}^{i-1}f[j]*g[j][i]
]