#include <bits/stdc++.h>
using namespace std;
#define f(i, a, b) for (int i = int(a); i < int(b); ++i)
#define vt vector
#define pb push_back
template < class A > void rd(vt < A > & v);
template < class T > void rd(T & x) {
cin >> x;
}
template < class H, class...T > void rd(H & h, T & ...t) {
rd(h);
rd(t...);
}
template < class A > void rd(vt < A > & x) {
for (auto & a: x) rd(a);
}
/*
* description :- polynomial hashing of strings.
* sources :- https://codeforces.com/contest/710/submission/102996468
* verification :- https://codeforces.com/contest/154/submission/120344887
*/
#ifdef int
static_assert(false, "do not define int");
#endif
template <
const unsigned & MOD >
struct _m_uint {
unsigned val;
_m_uint(int64_t v = 0) {
if (v < 0) v = v % MOD + MOD;
if (v >= MOD) v %= MOD;
val = unsigned(v);
}
_m_uint(uint64_t v) {
if (v >= MOD) v %= MOD;
val = unsigned(v);
}
_m_uint(int v): _m_uint(int64_t(v)) {}
_m_uint(unsigned v): _m_uint(uint64_t(v)) {}
explicit operator unsigned() const {
return val;
}
explicit operator int64_t() const {
return val;
}
explicit operator uint64_t() const {
return val;
}
explicit operator double() const {
return val;
}
explicit operator long double() const {
return val;
}
_m_uint & operator += (const _m_uint & other) {
val = val < MOD - other.val ? val + other.val : val - (MOD - other.val);
return *this;
}
_m_uint & operator -= (const _m_uint & other) {
val = val < other.val ? val + (MOD - other.val) : val - other.val;
return *this;
}
static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
#if!defined(_WIN32) || defined(_WIN64)
return unsigned(x % m);
#endif
// Optimized mod for Codeforces 32-bit machines.
// x must be less than 2^32 * m for this to work, so that x / m fits in an unsigned 32-bit int.
unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
unsigned quot, rem;
asm("divl %4\n": "=a"(quot), "=d"(rem): "d"(x_high), "a"(x_low), "r"(m));
return rem;
}
_m_uint & operator *= (const _m_uint & other) {
val = fast_mod(uint64_t(val) * other.val);
return *this;
}
_m_uint & operator /= (const _m_uint & other) {
return *this *= other.inv();
}
friend _m_uint operator + (const _m_uint & a,
const _m_uint & b) {
return _m_uint(a) += b;
}
friend _m_uint operator - (const _m_uint & a,
const _m_uint & b) {
return _m_uint(a) -= b;
}
friend _m_uint operator * (const _m_uint & a,
const _m_uint & b) {
return _m_uint(a) *= b;
}
friend _m_uint operator / (const _m_uint & a,
const _m_uint & b) {
return _m_uint(a) /= b;
}
_m_uint & operator++() {
val = val == MOD - 1 ? 0 : val + 1;
return *this;
}
_m_uint & operator--() {
val = val == 0 ? MOD - 1 : val - 1;
return *this;
}
_m_uint operator++(int) {
_m_uint before = * this;
++ * this;
return before;
}
_m_uint operator--(int) {
_m_uint before = * this;
-- * this;
return before;
}
_m_uint operator - () const {
return val == 0 ? 0 : MOD - val;
}
friend bool operator == (const _m_uint & a,
const _m_uint & b) {
return a.val == b.val;
}
friend bool operator != (const _m_uint & a,
const _m_uint & b) {
return a.val != b.val;
}
friend bool operator < (const _m_uint & a,
const _m_uint & b) {
return a.val < b.val;
}
friend bool operator > (const _m_uint & a,
const _m_uint & b) {
return a.val > b.val;
}
friend bool operator <= (const _m_uint & a,
const _m_uint & b) {
return a.val <= b.val;
}
friend bool operator >= (const _m_uint & a,
const _m_uint & b) {
return a.val >= b.val;
}
static
const int SAVE_INV = int(1e6) + 5;
static _m_uint save_inv[SAVE_INV];
static void prepare_inv() {
// Make sure MOD is prime, which is necessary for the inverse algorithm below.
for (int64_t p = 2; p * p <= MOD; p += p % 2 + 1) {
assert(MOD % p != 0);
}
save_inv[0] = 0;
save_inv[1] = 1;
for (int i = 2; i < SAVE_INV; i++) {
save_inv[i] = save_inv[MOD % i] * (MOD - MOD / i);
}
}
_m_uint inv() const {
if (save_inv[1] == 0) prepare_inv();
if (val < SAVE_INV) return save_inv[val];
_m_uint product = 1;
unsigned v = val;
while (v >= SAVE_INV) {
product *= MOD - MOD / v;
v = MOD % v;
}
return product * save_inv[v];
}
_m_uint pow(int64_t p) const {
if (p < 0) return inv().pow(-p);
_m_uint a = * this, result = 1;
while (p > 0) {
if (p & 1) result *= a;
p >>= 1;
if (p > 0) a *= a;
}
return result;
}
friend ostream & operator << (ostream & os,
const _m_uint & m) {
return os << m.val;
}
};
template <
const unsigned & MOD > _m_uint < MOD > _m_uint < MOD > ::save_inv[_m_uint < MOD > ::SAVE_INV];
auto random_address = [] {
char * p = new char;
delete p;
return uint64_t(p);
};
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));
// P = 2^32 - 13337 is a safe prime: both P and (P - 1) / 2 are prime.
extern
const unsigned HASH_P = unsigned(-13337); // hash prime
using hash_int = _m_uint < HASH_P > ;
using hash_t = uint64_t;
const uint64_t HASH_P2 = uint64_t(HASH_P) * HASH_P; // square of hash prime
const int HASH_COUNT = 2;
// Avoid multiplication bases near 0 or P - 1.
uniform_int_distribution < unsigned > MULT_DIST(unsigned(0.1 * HASH_P), unsigned(0.9 * HASH_P));
const hash_int HASH_MULT[] = {
MULT_DIST(rng),
MULT_DIST(rng)
}; // our bases
const hash_int HASH_INV[] = {
1 / HASH_MULT[0],
1 / HASH_MULT[1]
};
vector < hash_int > hash_pow[] = {
{
1
},
{
1
}
};
const int INF = int(1e9) + 5;
template < typename T_string = string >
struct string_hash {
static
const bool BUILD_REVERSE = false;
static uint64_t hash(const T_string & str) {
uint64_t result = 0;
for (int h = 0; h < HASH_COUNT; h++) {
uint64_t value = 1;
for (const auto & x: str) {
value = (uint64_t(HASH_MULT[h]) * value + x) % HASH_P;
}
result += value << (32 * h);
}
return result;
}
T_string str;
vector < hash_int > _prefix[HASH_COUNT];
vector < hash_int > _inv_prefix[HASH_COUNT];
string_hash() {
build({});
}
string_hash(const T_string & _str) {
build(_str);
}
int length() const {
return int(_prefix[0].size()) - 1;
}
template < typename T_char >
void add_char(const T_char & c) {
str.push_back(c);
for (int h = 0; h < HASH_COUNT; h++) {
_prefix[h].push_back(HASH_MULT[h] * _prefix[h].back() + c);
if (hash_pow[h].size() < _prefix[h].size()) {
hash_pow[h].push_back(HASH_MULT[h] * hash_pow[h].back());
}
if (BUILD_REVERSE) {
_inv_prefix[h].push_back((_inv_prefix[h].back() + c) * HASH_INV[h]);
}
}
}
void pop_char() {
str.pop_back();
for (int h = 0; h < HASH_COUNT; h++) {
_prefix[h].pop_back();
if (BUILD_REVERSE) {
_inv_prefix[h].pop_back();
}
}
}
void build(const T_string & _str) {
str = {};
str.reserve(_str.size());
for (int h = 0; h < HASH_COUNT; h++) {
hash_pow[h].reserve(_str.size() + 1);
_prefix[h] = {
0
};
_prefix[h].reserve(_str.size() + 1);
if (BUILD_REVERSE) {
_inv_prefix[h] = {
0
};
_inv_prefix[h].reserve(_str.size() + 1);
}
}
for (auto & c: _str) add_char(c);
}
uint64_t _single_hash(int h, int start, int end) const {
// Convert everything to `uint64_t` for speed. Note: we add hash_pow[length] to fix strings that start with 0.
uint64_t power = uint64_t(hash_pow[h][end - start]);
return (power + uint64_t(_prefix[h][end]) + HASH_P2 - uint64_t(_prefix[h][start]) * power) % HASH_P;
}
uint64_t substring_hash(int start, int end) const {
assert(0 <= start && start <= end && end <= length());
return _single_hash(0, start, end) + (HASH_COUNT > 1 ? _single_hash(1, start, end) << 32 : 0);
}
uint64_t complete_hash() const {
return substring_hash(0, length());
}
uint64_t _reverse_single_hash(int h, int start, int end) const {
// Convert everything to `uint64_t` for speed. Note: we add hash_pow[length] to fix strings that start with 0.
uint64_t power = uint64_t(hash_pow[h][end - start]);
return (power + uint64_t(_inv_prefix[h][end]) * power + HASH_P - uint64_t(_inv_prefix[h][start])) % HASH_P;
}
uint64_t reverse_substring_hash(int start, int end) const {
assert(0 <= start && start <= end && end <= length());
return _reverse_single_hash(0, start, end) + (HASH_COUNT > 1 ? _reverse_single_hash(1, start, end) << 32 : 0);
}
uint64_t reverse_complete_hash() const {
return reverse_substring_hash(0, length());
}
bool equal(int start1, int start2, int length) const {
return substring_hash(start1, start1 + length) == substring_hash(start2, start2 + length);
}
bool is_palindrome(int start, int end) const {
return substring_hash(start, end) == reverse_substring_hash(start, end);
}
int compare(int start1, int start2, int max_length = INF) const;
};
uint64_t concat_hashes(uint64_t hash1, uint64_t hash2, int len2) {
uint64_t hash1_low = hash1 & unsigned(-1);
uint64_t hash2_low = hash2 & unsigned(-1);
uint64_t power = uint64_t(hash_pow[0][len2]);
uint64_t combined = (hash1_low * power + hash2_low + HASH_P - power) % HASH_P;
if (HASH_COUNT > 1) {
hash1 >>= 32;
hash2 >>= 32;
power = uint64_t(hash_pow[1][len2]);
combined += (hash1 * power + hash2 + HASH_P - power) % HASH_P << 32;
}
return combined;
}
template < typename T_string >
int first_mismatch(const string_hash < T_string > & hash1, int start1,
const string_hash < T_string > & hash2, int start2, int max_length = INF) {
max_length = min({
max_length,
hash1.length() - start1,
hash2.length() - start2
});
static
const int FIRST = 5;
int first = min(max_length, FIRST);
for (int i = 0; i < first; i++) {
if (hash1.str[start1 + i] != hash2.str[start2 + i]) {
return i;
}
}
if (hash1.substring_hash(start1, start1 + max_length) == hash2.substring_hash(start2, start2 + max_length)) {
return max_length;
}
static
const int MANUAL = 15;
int low = first, high = max_length - 1;
while (high - low > MANUAL) {
int mid = (low + high + 1) / 2;
if (hash1.substring_hash(start1, start1 + mid) == hash2.substring_hash(start2, start2 + mid)) {
low = mid;
} else {
high = mid - 1;
}
}
for (int i = low; i < high; i++) {
if (hash1.str[start1 + i] != hash2.str[start2 + i]) {
return i;
}
}
return high;
}
template < typename T_string >
int hash_compare(const string_hash < T_string > & hash1, int start1,
const string_hash < T_string > & hash2, int start2, int max_length = INF) {
int mismatch = first_mismatch(hash1, start1, hash2, start2, max_length);
int length1 = min(hash1.length() - start1, max_length);
int length2 = min(hash2.length() - start2, max_length);
if (mismatch == min(length1, length2)) {
return length1 == length2 ? 0 : (length1 < length2 ? -1 : +1);
}
if (hash1.str[start1 + mismatch] == hash2.str[start2 + mismatch]) {
return 0;
}
return hash1.str[start1 + mismatch] < hash2.str[start2 + mismatch] ? -1 : +1;
}
template < typename T_string >
int string_hash < T_string > ::compare(int start1, int start2, int max_length) const {
return hash_compare( * this, start1, * this, start2, max_length);
}
template < class T > struct compress_1d_co_ordinates {
vector < T > values;
void add(T x) {
values.push_back(x);
return;
}
void gen() {
sort(values.begin(), values.end());
values.erase(unique(values.begin(), values.end()), values.end());
return;
}
int get(T x) {
int j = lower_bound(values.begin(), values.end(), x) - values.begin();
assert(values[j] == x);
return j;
}
void clear() {
values.clear();
return;
}
};
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n, m;
rd(n, m);
vector < string > s(n);
rd(s);
string_hash < string > string_h[2 * n];
f(i, 0, n) {
string_h[i].build(s[i] + s[i]);
string_h[i + n].build(s[i] + s[i]);
}
vt < int > best(m);
// rotote horizontally
for (int i = 0; i < m; ++i) {
vt < hash_t > _strings(2 * n);
vt < int > strings;
compress_1d_co_ordinates < hash_t > compress;
for (int j = 0; j < n; ++j) {
_strings[j] = _strings[n + j] = string_h[j].substring_hash(i, i + m);
compress.add(_strings[j]);
}
compress.gen();
for (auto & i: _strings) strings.pb(compress.get(i));
compress.clear();
string_hash < vector < int >> vector_h;
vector_h.build(strings);
int current_best = 0;
for (int j = 1; j < n; ++j) {
int k = first_mismatch(vector_h, current_best, vector_h, j, n);
if (k == n) continue;
int c = hash_compare(string_h[current_best + k], i, string_h[j + k], i, m);
assert(c != 0);
// if string 2 is small.
if (c == 1) current_best = j;
}
best[i] = current_best;
}
int x = 0;
for (int i = 1; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (string_h[best[x] + j].substring_hash(x, x + m) != string_h[best[i] + j].substring_hash(i, i + m)) {
int c = hash_compare(string_h[best[x] + j], x, string_h[best[i] + j], i, m);
assert(c != 0);
// if string 2 is small
if (c == 1) x = i;
break;
}
}
}
f(i, 0, n) {
f(j, 0, m) {
cout << s[(i + best[x]) % n][(j + x) % m];
}
cout << "\n";
}
}
