Today Alice designs a game using these drawings in her memory. First, she matches K+1 colors appears in the picture to K+1 different integers(from 0 to K). After that, she slices the drawing into grids and there are N rows and M columns. Each grid has an integer on it(from 0 to K) representing the color on the corresponding position in the original drawing. Alice wants to share the wonderful drawings with Bob and she tells Bob the size of the drawing, the number of different colors, and the sum of integers on each row and each column. Bob has to redraw the drawing with Alice's information. Unfortunately, somtimes, the information Alice offers is wrong because of Alice's poor math. And sometimes, Bob can work out multiple different drawings using the information Alice provides. Bob gets confused and he needs your help. You have to tell Bob if Alice's information is right and if her information is right you should also tell Bob whether he can get a unique drawing.
For each testcase, the first line contains three integers N(1 ≤ N ≤ 400) , M(1 ≤ M ≤ 400) and K(1 ≤ K ≤ 40).
N integers are given in the second line representing the sum of N rows.
M integers are given in the third line representing the sum of M columns.
The input is terminated by EOF.
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <queue>
#include <numeric>
using namespace std;
typedef long long LL; const int MAXN = ;
const int MAXV = MAXN << ;
const int MAXE = * MAXN * MAXN;
const int INF = 0x3f3f3f3f; struct ISAP {
int head[MAXV], cur[MAXV], gap[MAXV], dis[MAXV], pre[MAXV];
int to[MAXE], next[MAXE], flow[MAXE];
int n, ecnt, st, ed; void init(int n) {
this->n = n;
memset(head + , -, n * sizeof(int));
ecnt = ;
} void add_edge(int u, int v, int c) {
to[ecnt] = v; flow[ecnt] = c; next[ecnt] = head[u]; head[u] = ecnt++;
to[ecnt] = u; flow[ecnt] = ; next[ecnt] = head[v]; head[v] = ecnt++;
} void bfs() {
memset(dis + , 0x3f, n * sizeof(int));
queue<int> que; que.push(ed);
dis[ed] = ;
while(!que.empty()) {
int u = que.front(); que.pop();
gap[dis[u]]++;
for(int p = head[u]; ~p; p = next[p]) {
int v = to[p];
if(flow[p ^ ] && dis[u] + < dis[v]) {
dis[v] = dis[u] + ;
que.push(v);
}
}
}
} int max_flow(int ss, int tt) {
st = ss, ed = tt;
int ans = , minFlow = INF;
for(int i = ; i <= n; ++i) {
cur[i] = head[i];
gap[i] = ;
}
bfs();
int u = pre[st] = st;
while(dis[st] < n) {
bool flag = false;
for(int &p = cur[u]; ~p; p = next[p]) {
int v = to[p];
if(flow[p] && dis[u] == dis[v] + ) {
flag = true;
minFlow = min(minFlow, flow[p]);
pre[v] = u;
u = v;
if(u == ed) {
ans += minFlow;
while(u != st) {
u = pre[u];
flow[cur[u]] -= minFlow;
flow[cur[u] ^ ] += minFlow;
}
minFlow = INF;
}
break;
}
}
if(flag) continue;
int minDis = n - ;
for(int p = head[u]; ~p; p = next[p]) {
int &v = to[p];
if(flow[p] && dis[v] < minDis) {
minDis = dis[v];
cur[u] = p;
}
}
if(--gap[dis[u]] == ) break;
++gap[dis[u] = minDis + ];
u = pre[u];
}
return ans;
} int stk[MAXV], top;
bool sccno[MAXV], vis[MAXV]; bool dfs(int u, int f, bool flag) {
vis[u] = true;
stk[top++] = u;
for(int p = head[u]; ~p; p = next[p]) if(flow[p]) {
int v = to[p];
if(v == f) continue;
if(!vis[v]) {
if(dfs(v, u, flow[p ^ ])) return true;
} else if(!sccno[v]) return true;
}
if(!flag) {
while(true) {
int x = stk[--top];
sccno[x] = true;
if(x == u) break;
}
}
return false;
} bool acycle() {
memset(sccno + , , n * sizeof(bool));
memset(vis + , , n * sizeof(bool));
top = ;
return dfs(ed, , );
}
} G; int row[MAXN], col[MAXN];
int mat[MAXN][MAXN];
int n, m, k, ss, tt; void solve() {
int sumr = accumulate(row + , row + n + , );
int sumc = accumulate(col + , col + m + , );
if(sumr != sumc) {
puts("Impossible");
return ;
}
int res = G.max_flow(ss, tt);
if(res != sumc) {
puts("Impossible");
return ;
}
if(G.acycle()) {
puts("Not Unique");
} else {
puts("Unique");
for(int i = ; i <= n; ++i) {
for(int j = ; j < m; ++j) printf("%d ", G.flow[mat[i][j]]);
printf("%d\n", G.flow[mat[i][m]]);
}
}
} int main() {
while(scanf("%d%d%d", &n, &m, &k) != EOF) {
for(int i = ; i <= n; ++i) scanf("%d", &row[i]);
for(int i = ; i <= m; ++i) scanf("%d", &col[i]);
ss = n + m + , tt = n + m + ;
G.init(tt);
for(int i = ; i <= n; ++i) G.add_edge(ss, i, row[i]);
for(int i = ; i <= m; ++i) G.add_edge(n + i, tt, col[i]);
for(int i = ; i <= n; ++i) {
for(int j = ; j <= m; ++j) {
mat[i][j] = G.ecnt ^ ;
G.add_edge(i, n + j, k);
}
}
solve();
}
}