#include <bits/stdc++.h>
using namespace std;
using lint = long long;
const lint mod = 1e9 + 7;
#define all(x) (x).begin(), (x).end()
#define bitcount(n) __builtin_popcountl((lint)(n))
#define fcout cout << fixed << setprecision(15)
#define highest(x) (63 - __builtin_clzl(x))
template<class T> inline void YES(T condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; }
template<class T> inline void Yes(T condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
template<class T = string, class U = char>int character_count(T text, U character){ int ans = 0; for(U i: text){ ans += (i == character); } return ans; }
lint power(lint base, lint exponent, lint module){ if(exponent % 2){ return power(base, exponent - 1, module) * base % module; }else if(exponent){ lint root_ans = power(base, exponent / 2, module); return root_ans * root_ans % module; }else{ return 1; }}
struct position{ int y, x; }; position mv[4] = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}; // double euclidean(position first, position second){ return sqrt((second.x - first.x) * (second.x - first.x) + (second.y - first.y) * (second.y - first.y)); }
template<class T, class U> string to_string(pair<T, U> x){ return to_string(x.first) + "," + to_string(x.second); } string to_string(string x){ return x; }
template<class itr> void array_output(itr start, itr goal){ string ans; for(auto i = start; i != goal; i++) ans += to_string(*i) + " "; if(!ans.empty()) ans.pop_back(); cout << ans << endl; }
template<class itr> void cins(itr first, itr last){ for(auto i = first; i != last; i++){ cin >> (*i); } }
template<class T> T gcd(T a, T b){ if(a && b){ return gcd(min(a, b), max(a, b) % min(a, b)); }else{ return a; }} template<class T> T lcm(T a, T b){ return a / gcd(a, b) * b; }
struct combination{ vector<lint> fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2, mod); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } lint C(int p, int q) const{ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } };
template<class itr> bool next_sequence(itr first, itr last, int max_bound){ itr now = last; while(now != first){ now--; (*now)++; if((*now) == max_bound){ (*now) = 0; }else{ return true; } } return false; }

lint full_fact = 1000000006;
vector<lint> fact_arr = {1, 641102369, 578095319, 5832229, 259081142, 974067448, 316220877, 690120224, 251368199, 980250487, 682498929, 134623568, 95936601, 933097914, 167332441, 598816162, 336060741, 248744620, 626497524, 288843364, 491101308, 245341950, 565768255, 246899319, 968999, 586350670, 638587686, 881746146, 19426633, 850500036, 76479948, 268124147, 842267748, 886294336, 485348706, 463847391, 544075857, 898187927, 798967520, 82926604, 723816384, 156530778, 721996174, 299085602, 323604647, 172827403, 398699886, 530389102, 294587621, 813805606, 67347853, 497478507, 196447201, 722054885, 228338256, 407719831, 762479457, 746536789, 811667359, 778773518, 27368307, 438371670, 59469516, 5974669, 766196482, 606322308, 86609485, 889750731, 340941507, 371263376, 625544428, 788878910, 808412394, 996952918, 585237443, 1669644, 361786913, 480748381, 595143852, 837229828, 199888908, 526807168, 579691190, 145404005, 459188207, 534491822, 439729802, 840398449, 899297830, 235861787, 888050723, 656116726, 736550105, 440902696, 85990869, 884343068, 56305184, 973478770, 168891766, 804805577, 927880474, 876297919, 934814019, 676405347, 567277637, 112249297, 44930135, 39417871, 47401357, 108819476, 281863274, 60168088, 692636218, 432775082, 14235602, 770511792, 400295761, 697066277, 421835306, 220108638, 661224977, 261799937, 168203998, 802214249, 544064410, 935080803, 583967898, 211768084, 751231582, 972424306, 623534362, 335160196, 243276029, 554749550, 60050552, 797848181, 395891998, 172428290, 159554990, 887420150, 970055531, 250388809, 487998999, 856259313, 82104855, 232253360, 513365505, 244109365, 1559745, 695345956, 261384175, 849009131, 323214113, 747664143, 444090941, 659224434, 80729842, 570033864, 664989237, 827348878, 195888993, 576798521, 457882808, 731551699, 212938473, 509096183, 827544702, 678320208, 677711203, 289752035, 66404266, 555972231, 195290384, 97136305, 349551356, 785113347, 83489485, 66247239, 52167191, 307390891, 547665832, 143066173, 350016754, 917404120, 296269301, 996122673, 23015220, 602139210, 748566338, 187348575, 109838563, 574053420, 105574531, 304173654, 542432219, 34538816, 325636655, 437843114, 630621321, 26853683, 933245637, 616368450, 238971581, 511371690, 557301633, 911398531, 848952161, 958992544, 925152039, 914456118, 724691727, 636817583, 238087006, 946237212, 910291942, 114985663, 492237273, 450387329, 834860913, 763017204, 368925948, 475812562, 740594930, 45060610, 806047532, 464456846, 172115341, 75307702, 116261993, 562519302, 268838846, 173784895, 243624360, 61570384, 481661251, 938269070, 95182730, 91068149, 115435332, 495022305, 136026497, 506496856, 710729672, 113570024, 366384665, 564758715, 270239666, 277118392, 79874094, 702807165, 112390913, 730341625, 103056890, 677948390, 339464594, 167240465, 108312174, 839079953, 479334442, 271788964, 135498044, 277717575, 591048681, 811637561, 353339603, 889410460, 839849206, 192345193, 736265527, 316439118, 217544623, 788132977, 618898635, 183011467, 380858207, 996097969, 898554793, 335353644, 54062950, 611251733, 419363534, 965429853, 160398980, 151319402, 990918946, 607730875, 450718279, 173539388, 648991369, 970937898, 500780548, 780122909, 39052406, 276894233, 460373282, 651081062, 461415770, 358700839, 643638805, 560006119, 668123525, 686692315, 673464765, 957633609, 199866123, 563432246, 841799766, 385330357, 504962686, 954061253, 128487469, 685707545, 299172297, 717975101, 577786541, 318951960, 773206631, 306832604, 204355779, 573592106, 30977140, 450398100, 363172638, 258379324, 472935553, 93940075, 587220627, 776264326, 793270300, 291733496, 522049725, 579995261, 335416359, 142946099, 472012302, 559947225, 332139472, 499377092, 464599136, 164752359, 309058615, 86117128, 580204973, 563781682, 954840109, 624577416, 895609896, 888287558, 836813268, 926036911, 386027524, 184419613, 724205533, 403351886, 715247054, 716986954, 830567832, 383388563, 68409439, 6734065, 189239124, 68322490, 943653305, 405755338, 811056092, 179518046, 825132993, 343807435, 985084650, 868553027, 148528617, 160684257, 882148737, 591915968, 701445829, 529726489, 302177126, 974886682, 241107368, 798830099, 940567523, 11633075, 325334066, 346091869, 115312728, 473718967, 218129285, 878471898, 180002392, 699739374, 917084264, 856859395, 435327356, 808651347, 421623838, 105419548, 59883031, 322487421, 79716267, 715317963, 429277690, 398078032, 316486674, 384843585, 940338439, 937409008, 940524812, 947549662, 833550543, 593524514, 996164327, 987314628, 697611981, 636177449, 274192146, 418537348, 925347821, 952831975, 893732627, 1277567, 358655417, 141866945, 581830879, 987597705, 347046911, 775305697, 125354499, 951540811, 247662371, 343043237, 568392357, 997474832, 209244402, 380480118, 149586983, 392838702, 309134554, 990779998, 263053337, 325362513, 780072518, 551028176, 990826116, 989944961, 155569943, 596737944, 711553356, 268844715, 451373308, 379404150, 462639908, 961812918, 654611901, 382776490, 41815820, 843321396, 675258797, 845583555, 934281721, 741114145, 275105629, 666247477, 325912072, 526131620, 252551589, 432030917, 554917439, 818036959, 754363835, 795190182, 909210595, 278704903, 719566487, 628514947, 424989675, 321685608, 50590510, 832069712, 198768464, 702004730, 99199382, 707469729, 747407118, 302020341, 497196934, 5003231, 726997875, 382617671, 296229203, 183888367, 703397904, 552133875, 732868367, 350095207, 26031303, 863250534, 216665960, 561745549, 352946234, 784139777, 733333339, 503105966, 459878625, 803187381, 16634739, 180898306, 68718097, 985594252, 404206040, 749724532, 97830135, 611751357, 31131935, 662741752, 864326453, 864869025, 167831173, 559214642, 718498895, 91352335, 608823837, 473379392, 385388084, 152267158, 681756977, 46819124, 313132653, 56547945, 442795120, 796616594, 256141983, 152028387, 636578562, 385377759, 553033642, 491415383, 919273670, 996049638, 326686486, 160150665, 141827977, 540818053, 693305776, 593938674, 186576440, 688809790, 565456578, 749296077, 519397500, 551096742, 696628828, 775025061, 370732451, 164246193, 915265013, 457469634, 923043932, 912368644, 777901604, 464118005, 637939935, 956856710, 490676632, 453019482, 462528877, 502297454, 798895521, 100498586, 699767918, 849974789, 811575797, 438952959, 606870929, 907720182, 179111720, 48053248, 508038818, 811944661, 752550134, 401382061, 848924691, 764368449, 34629406, 529840945, 435904287, 26011548, 208184231, 446477394, 206330671, 366033520, 131772368, 185646898, 648711554, 472759660, 523696723, 271198437, 25058942, 859369491, 817928963, 330711333, 724464507, 437605233, 701453022, 626663115, 281230685, 510650790, 596949867, 295726547, 303076380, 465070856, 272814771, 538771609, 48824684, 951279549, 939889684, 564188856, 48527183, 201307702, 484458461, 861754542, 326159309, 181594759, 668422905, 286273596, 965656187, 44135644, 359960756, 936229527, 407934361, 267193060, 456152084, 459116722, 124804049, 262322489, 920251227, 816929577, 483924582, 151834896, 167087470, 490222511, 903466878, 361583925, 368114731, 339383292, 388728584, 218107212, 249153339, 909458706, 322908524, 202649964, 92255682, 573074791, 15570863, 94331513, 744158074, 196345098, 334326205, 9416035, 98349682, 882121662, 769795511, 231988936, 888146074, 137603545, 582627184, 407518072, 919419361, 909433461, 986708498, 310317874, 373745190, 263645931, 256853930, 876379959, 702823274, 147050765, 308186532, 175504139, 180350107, 797736554, 606241871, 384547635, 273712630, 586444655, 682189174, 666493603, 946867127, 819114541, 502371023, 261970285, 825871994, 126925175, 701506133, 314738056, 341779962, 561011609, 815463367, 46765164, 49187570, 188054995, 957939114, 64814326, 933376898, 329837066, 338121343, 765215899, 869630152, 978119194, 632627667, 975266085, 435887178, 282092463, 129621197, 758245605, 827722926, 201339230, 918513230, 322096036, 547838438, 985546115, 852304035, 593090119, 689189630, 555842733, 567033437, 469928208, 212842957, 117842065, 404149413, 155133422, 663307737, 208761293, 206282795, 717946122, 488906585, 414236650, 280700600, 962670136, 534279149, 214569244, 375297772, 811053196, 922377372, 289594327, 219932130, 211487466, 701050258, 398782410, 863002719, 27236531, 217598709, 375472836, 810551911, 178598958, 247844667, 676526196, 812283640, 863066876, 857241854, 113917835, 624148346, 726089763, 564827277, 826300950, 478982047, 439411911, 454039189, 633292726, 48562889, 802100365, 671734977, 945204804, 508831870, 398781902, 897162044, 644050694, 892168027, 828883117, 277714559, 713448377, 624500515, 590098114, 808691930, 514359662, 895205045, 715264908, 628829100, 484492064, 919717789, 513196123, 748510389, 403652653, 574455974, 77123823, 172096141, 819801784, 581418893, 15655126, 15391652, 875641535, 203191898, 264582598, 880691101, 907800444, 986598821, 340030191, 264688936, 369832433, 785804644, 842065079, 423951674, 663560047, 696623384, 496709826, 161960209, 331910086, 541120825, 951524114, 841656666, 162683802, 629786193, 190395535, 269571439, 832671304, 76770272, 341080135, 421943723, 494210290, 751040886, 317076664, 672850561, 72482816, 493689107, 135625240, 100228913, 684748812, 639655136, 906233141, 929893103, 277813439, 814362881, 562608724, 406024012, 885537778, 10065330, 60625018, 983737173, 60517502, 551060742, 804930491, 823845496, 727416538, 946421040, 678171399, 842203531, 175638827, 894247956, 538609927, 885362182, 946464959, 116667533, 749816133, 241427979, 871117927, 281804989, 163928347, 563796647, 640266394, 774625892, 59342705, 256473217, 674115061, 918860977, 322633051, 753513874, 393556719, 304644842, 767372800, 161362528, 754787150, 627655552, 677395736, 799289297, 846650652, 816701166, 687265514, 787113234, 358757251, 701220427, 607715125, 245795606, 600624983, 10475577, 728620948, 759404319, 36292292, 491466901, 22556579, 114495791, 647630109, 586445753, 482254337, 718623833, 763514207, 66547751, 953634340, 351472920, 308474522, 494166907, 634359666, 172114298, 865440961, 364380585, 921648059, 965683742, 260466949, 117483873, 962540888, 237120480, 620531822, 193781724, 213092254, 107141741, 602742426, 793307102, 756154604, 236455213, 362928234, 14162538, 753042874, 778983779, 25977209, 49389215, 698308420, 859637374, 49031023, 713258160, 737331920, 923333660, 804861409, 83868974, 682873215, 217298111, 883278906, 176966527, 954913, 105359006, 390019735, 10430738, 706334445, 315103615, 567473423, 708233401, 48160594, 946149627, 346966053, 281329488, 462880311, 31503476, 185438078, 965785236, 992656683, 916291845, 881482632, 899946391, 321900901, 512634493, 303338827, 121000338, 967284733, 492741665, 152233223, 165393390, 680128316, 917041303, 532702135, 741626808, 496442755, 536841269, 131384366, 377329025, 301196854, 859917803, 676511002, 373451745, 847645126, 823495900, 576368335, 73146164, 954958912, 847549272, 241289571, 646654592, 216046746, 205951465, 3258987, 780882948, 822439091, 598245292, 869544707, 698611116};

lint inv(lint x){
    assert(x);
    return power(x, mod - 2, mod);
}

lint fact(lint n){
    n %= mod;
    lint ans = fact_arr[n / int(1e6)];
    for(lint i = n / int(1e6) * int(1e6) + 1; i <= n; i++){
        ans = ans * i % mod;
    }
    return ans;
}

lint combination(lint n, lint r){
    if(n / mod > r / mod + (n - r) / mod){
        return 0;
    }
    return fact(n) * inv(fact(r)) % mod * inv(fact(n - r)) % mod;
}

int main(){
    lint N, M, K;
    cin >> N >> M >> K;
    lint ans = 0, sum = 0;
    for(lint i = 0; i < N; i++){
        sum += i * (N - i) % mod;
    }
    sum = sum * M % mod * M % mod;
    ans += sum;
    sum = 0;
    for(lint i = 0; i < M; i++){
        sum += i * (M - i) % mod;
    }
    sum = sum * N % mod * N % mod;
    ans += sum;
    ans %= mod;
    cout << ans * combination(N * M - 2, K - 2) % mod << endl;
}


Measured memory_bytes: 256