448_D. Multiplication Table_10288
Bizon the Champion isn't just charming, he also is very smart.

While some of us were learning the multiplication table, Bizon the Champion had fun in his own manner. Bizon the Champion painted an n × m multiplication table, where the element on the intersection of the i-th row and j-th column equals i·j (the rows and columns of the table are numbered starting from 1). Then he was asked: what number in the table is the k-th largest number? Bizon the Champion always answered correctly and immediately. Can you repeat his success?

Consider the given multiplication table. If you write out all n·m numbers from the table in the non-decreasing order, then the k-th number you write out is called the k-th largest number.

Input

The single line contains integers n, m and k (1 ≤ n, m ≤ 5·105; 1 ≤ k ≤ n·m).

Output

Print the k-th largest number in a n × m multiplication table.

Examples

Input

2 2 2


Output

2


Input

2 3 4


Output

3


Input

1 10 5


Output

5

Note

A 2 × 3 multiplication table looks like this:
    
    
      
    1 2 3  
    2 4 6  
      
    
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC optimize("Os")
using namespace std;
template <typename T, typename K>
inline void umax(T &a, K b) {
  a = max(a, (T)b);
}
template <typename T, typename K>
inline void umin(T &a, K b) {
  a = min(a, (T)b);
}
const int32_t N = 8e6;
const long long INF = 1e16 + 10;
const long double EPS = 1e-6;
const long long II = 1e9 + 10;
const long long MOD = 1e9 + 7;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, m, k;
  cin >> n >> m >> k;
  long long ll = 0, rr = n * m + 1;
  while (ll < rr) {
    long long mm = (ll + rr) >> 1LL;
    long long cnt = 0;
    for (long long i = 1; i <= n; i++) {
      cnt += min(m, mm / i);
    }
    if (cnt < k)
      ll = mm + 1;
    else
      rr = mm;
  }
  cout << ll << endl;
}

2 3 4
 2 2 2
 1 10 5
 143 1735 246128
 3082 23173 68350097
 264 3 775
 3 48 30
 3119 3 7305
 302 39 4623
 41 246624 2596292
 12 28 127
 357 184324 28748161
 20 2222 11312
 48 33111 5809
 3 3 9
 183656 409931 42943608085
 35531 340928 9207622511
 472 15 932
 2396 24 55229
 345 423483 40390152
 37107 4 28350
 40716 482 14569037
 32 11568 36460
 499975 499981 12345
 38939 3 6757
 314 32 3903
 123 37349 4224986
 1165 34678 7211566
 18 459 7733
 3 3 3
 201542 4833 512478332
 25 1155 9981
 3 4175 661
 226111 2 359116
 2315 1673 225263
 318377 38 7214261
 370768 123 15161219
 4460 377 1197310
 5 385 1296
 3191 454046 718852491
 23808 3322 48603931
 499997 499989 248758432143
 1 500000 74747
 1 454 340
 500000 500000 250000000000
 1426 26259 37212278
 10 1 7
 46068 31 424079
 4 1796 2564
 2 28 49
 5 353491 107977
 25 127045 1458997
 318 440 57023
 5 17136 9220
 5 1 2
 1 2 1
 1487 3295 736705
 149281 382 51428462
 2930 491026 923941798
 110941 47433 2098952903
 32 12 132
 17980 28231 221639883
 48 40 937
 10657 3 9816
 2115 384 385536
 4775 3 7798
 3 3 2
 306 433 25754
 187 425625 25103321
 10 10 33
 1 1 1
 366 45769 5885721
 41 4600 39636
 27 24692 71714
 3 355632 94220
 427 46704 7152399
 2 44 36
 1140 18 11371
 283422 407789 73398688052
 447 4446 802918
 500000 500000 888888
 37203 219 2355222
 20296 4388 29300901
 48922 150 653002
 500000 500000 1
 136614 3211 364472869
 3 3 5
 4 25555 45556
 43737 111829 865416726
 204791 41 8382971
 26 5 79
 12090 2766 12261436
 38 127 1330
 339697 4 1259155
 47 5 157
 2376 308 665957
 3571 3828 7070865
 403 363 932
 19618 16 313726
 132 3890 439379
 252 5 672
 3 3 1
 500000 1 47474
 46 356143 2399416
 16148 39736 239320912
 2 2 4
 2 33975 17369
 1 450 399
 45 317 6079
 495 3 17
 175869 39014 3201917805
 423029 1365 126620483
 118728 168631 16269281609
 139863 21 1834174
 1035 2 2055
 1274 295345 301511265
 27824 40 906786
 313975 448 85041752
 404625 2 132619
 4 194790 114613
 3 3 8
 4313 40 86640
 397356 10518 874806404
 29699 38801 37684232
 1 3304 218
 21980 353130 2233068545
 40 2 3
 3082 23173 53119773
 3 76 30
 61 246624 2596292
 15 28 127
 619 184324 28748161
 6 2222 11312
 48 33111 7785
 3 4 9
 172200 409931 42943608085
 35531 340928 2716234336
 472 17 932
 2396 24 20015
 345 423483 18122417
 33413 4 28350
 40716 482 3341282
 32 2773 36460
 618224 499981 12345
 33640 3 6757
 314 32 4530
 1676 34678 7211566
 18 662 7733
 3 3 6
 201542 4833 604160976
 25 2263 9981
 3 4175 635
 2315 1133 225263
 318377 70 7214261
 370768 123 20443991
 4460 737 1197310
 5 417 1296
 5615 454046 718852491
 23808 3322 51703041
 1 500000 146756
 1729 26259 37212278
 7 1 7
 46068 31 493291
 4 28 49
 5 353491 150324
 25 127045 708453
 318 333 57023
 5 17136 13137
 1 3 1
 1487 3295 740475
 4890 491026 923941798
 84869 47433 2098952903
 32 17 132
 48 36 937
 10657 3 8154
 2994 3 7798
 2 3 2
 306 470 25754
 187 345731 25103321
 5 10 33
 366 45769 10996431
 41 4600 57212
 13 24692 71714
 3 57376 94220
 729 46704 7152399
 1140 18 1067

3 2 5 218316 51543000 741 17 5024 1589 751716 49 9992350 3502 1308 9 17438143800 4761654318 283 43102 11441760 13608 7363656 8988 1634 3686 1345 2895390 1745254 5684 2 197440230 3318 361 266010 40950 3108710 4677246 581462 711 267275676 20824476 225563648440 74747 340 250000000000 33359110 7 131352 1232 42 47290 548779 19203 4039 2 1 169290 33762615 409544625 693548595 50 76707084 364 5355 140250 4254 2 6500 7534560 14 1 1841004 10865 18432 51393 2256408 24 4830 32237937640 268036 77856 681502 8862304 135716 1 209750632 3 21868 208223208 8020256 42 3894264 404 993876 87 445248 2696688 175 311296 265096 328 1 47474 598032 76569666 4 11580 399 2160 10 1148848775 32780826 9092195490 833220 2040 165699050 518185 36070940 88413 55015 6 33496 222468766 6032628 218 638445948 2 26860784
 17
 657978
 45
 7840179
 7536
 1751
 6
 18254872778
 707278794
 273
 6693
 3982823
 13608
 800358
 12852
 1634
 3686
 1674
 1567035
 3654
 4
 260631120
 2745
 347
 44760
 2225930
 7259742
 379874
 686
 203943730
 23248400
 146756
 21036587
 7
 161856
 24
 65836
 206472
 22454
 5754
 1
 170414
 300089777
 803938137
 44
 390
 4448
 5766
 2
 6336
 8259042
 20
 4973125
 17586
 22552
 51393
 1828267
 308
