P16364 [HackerEarth] Given Two matrix A and B of some order RXC. Both matrix contains elements from 1 to R*C . Matrix A contains elements in Row-major order while Matrix B contains elements in Column-major
普及-
题目描述

Given Two matrix A and B of some order RXC. Both matrix contains elements from 1 to R*C . Matrix A contains elements in Row-major order while Matrix B contains elements in Column-major order .you are asked to answer a very simple question what is the trace of the matrix formed by the addition of A and B.
Here, Trace of the matrix is defined as P[1][1] + P[2][2]... + P[min(n,m)][min(n,m)] for any rectangular matrix P.

INPUT:
First line of input contains T denoting number of test cases. Each test case consists of single line only containing two integers denoting order of matrix R and C.

OUTPUT:
output consists of T lines each containing answer to the corresponding test cases.

CONSTRAINTS
T ≤ 10^5
1 ≤ R,C ≤ 10^6

SAMPLE INPUT
2
3 3
1 2

SAMPLE OUTPUT
30
2

Explanation

For first input ,
the two matrices A and B will be : 

1 2 3

A = 4 5 6
7 8 9

1 4 7

B = 2 5 8
3 6 9

  2 6 10

A+B = 6 10 14
10 14 18

There , the trace of (A+B) matrix is 2 + 10 + 18 = 30

Similarly , answer can be found for the second input also.

输入格式

见题面

输出格式

见题面

样例输入
1000 12 89 77 24 12 55 3 80 90 66 89 62 43 85 21 2 99 78 79 39 15 65 8 78 50 10 7 38 82 23 93 26 1 20 78 54 13 70 36 97 36 55 63 37 60 50 45 76 26 78 33 76 1 27 49 51 61 49 46 85 3 24 91 74 84 9 36 46 77 72 43 93 42 16 35 65 23 29 23 64 5 8 62 14 13 42 64 69 94 32 30 44 4 89 94 56 1 19 77 59 54 52 57 40 52 69 35 34 37 99 90 24 71 43 76 60 12 25 34 73 70 42 67 98 35 62 5 89 50 25 63 99 9 58 17 53 87 8 55 56 84 4 82 58 12 67 6 6 23 19 96 51 59 23 27 86 13 64 39 94 32 79 21 92 73 42 29 19 37 82 31 67 73 29 44 52 39 9 10 8 90 8 22 79 6 63 39 75 59 90 33 83 32 80 76 18 94 2 92 73 4 100 58 58 28 85 4 54 16 30 68 84 79 88 75 14 77 22 72 89 27 35 14 14 90 55 1 26 19 38 29 27 52 60 40 73 81 48 39 59 86 16 73 85 54 16 36 76 99 41 17 88 88 25 75 51 94 91 14 96 73 82 10 7 93 9 66 64 22 55 4 49 29 88 96 50 50 43 33 24 77 41 3 96 14 29 17 48 78 5 11 64 81 52 62 29 15 72 90 38 42 59 91 64 98 95 74 63 59 83 42 6 59 41 99 73 84 53 76 97 50 86 16 72 44 32 26 99 69 42 99 88 19 48 23 94 92 32 51 12 98 62 79 28 63 100 25 68 63 77 2 8 80 51 45 35 92 13 97 68 82 18 50 32 39 98 12 45 78 11 34 40 71 43 48 65 89 35 9 3 4 74 65 52 3 22 11 55 73 85 52 39 4 40 66 82 31 52 45 39 33 91 33 47 1 64 54 2 38 16 34 59 20 82 25 13 95 49 27 32 45 79 44 81 62 24 14 83 90 4 92 68 37 97 87 54 91 82 97 18 38 51 75 99 44 23 21 28 65 58 3 25 86 62 74 89 18 60 68 11 82 51 1 79 46 69 66 8 83 30 98 18 87 13 14 83 50 40 81 53 47 19 5 43 35 16 64 63 7 7 27 57 39 69 100 6 75 3 43 13 67 73 28 56 26 98 96 50 35 66 25 38 88 16 23 12 55 27 63 69 29 11 57 92 60 70 37 53 87 27 50 53 24 36 81 67 16 51 70 32 47 47 34 74 64 96 71 80 62 100 84 42 11 21 45 71 92 22 2 81 40 41 87 94 27 69 96 67 55 22 43 2 50 94 60 29 60 26 89 65 7 33 76 93 87 19 55 26 99 89 67 67 73 88 48 51 20 98 55 48 27 34 60 53 70 91 86 13 64 46 27 12 86 31 92 64 81 12 96 61 87 17 57 12 6 56 79 41 67 46 61 77 56 97 60 58 55 11 98 74 14 9 6 57 73 6 44 10 52 24 16 10 54 53 8 99 97 64 86 18 7 60 51 11 22 91 12 26 96 38 61 2 12 27 42 85 85 13 49 48 63 100 31 94 87 38 32 31 27 39 11 93 73 6 45 12 47 72 80 22 39 74 43 92 53 50 22 48 72 63 24 23 32 60 15 9 4 7 64 27 14 57 43 38 45 21 70 4 73 79 58 9 13 70 1 88 35 11 32 4 29 94 14 51 47 93 41 98 30 99 36 11 77 65 31 85 22 52 84 18 27 56 65 69 12 12 8 82 13 90 31 23 52 64 2 62 87 72 95 41 47 75 63 56 40 35 19 43 64 95 88 34 100 2 1 5 3 48 9 90 1 96 93 44 36 21 54 18 82 41 22 66 98 7 3 99 74 32 62 79 22 15 31 52 11 26 51 49 50 47 71 7 76 35 2 72 21 88 60 84 19 7 18 32 50 8 36 44 97 17 14 88 73 29 54 13 1 80 42 13 57 49 74 36 22 66 24 32 100 37 23 54 79 84 58 94 36 10 20 10 60 76 92 60 50 41 5 72 58 71 56 61 23 55 38 18 34 51 63 44 21 69 45 47 8 10 16 3 33 37 80 7 49 4 2 47 49 83 42 95 93 100 96 35 56 46 93 80 72 88 13 49 43 11 15 62 34 78 9 81 86 55 77 30 31 19 33 99 96 82 81 53 67 37 10 75 69 49 23 18 93 65 74 100 23 14 66 35 1 39 65 88 19 29 58 52 56 51 9 3 36 89 98 19 4 43 25 54 10 19 22 74 99 3 72 25 55 46 51 28 47 18 12 17 80 24 37 99 70 86 61 43 70 67 71 81 97 30 100 37 10 36 7 66 64 47 56 17 53 71 1 26 99 26 2 34 76 97 15 24 79 77 40 86 47 68 7 88 45 32 51 72 57 73 89 57 14 67 60 71 51 52 93 10 96 66 90 43 91 31 90 12 28 88 31 77 89 17 75 88 93 57 57 36 59 76 90 2 9 34 6 68 30 64 33 61 57 61 16 36 80 6 61 8 84 12 98 97 78 76 47 42 44 9 5 91 19 87 4 76 6 91 90 19 27 3 79 16 6 25 5 26 7 76 24 27 2 69 57 83 11 69 42 93 67 94 60 90 10 23 45 60 2 11 82 6 33 18 86 43 90 29 90 20 31 64 25 32 85 27 24 97 96 5 26 76 79 69 80 53 97 85 27 83 66 31 28 54 32 16 46 7 66 30 74 2 5 14 69 39 99 79 66 45 43 53 85 13 28 45 75 39 4 92 14 28 12 42 70 11 60 76 45 76 95 58 85 88 32 13 5 38 60 77 91 63 17 84 48 74 2 82 69 60 69 82 84 6 68 6 94 37 22 2 91 80 87 31 32 70 28 58 78 82 34 77 64 71 5 24 87 92 74 96 33 73 58 44 78 6 36 84 90 82 100 8 6 34 57 98 36 11 61 20 52 77 96 30 18 28 12 28 49 76 77 58 92 85 97 61 58 84 3 89 16 32 25 63 89 97 89 94 35 15 79 80 37 75 55 24 82 100 7 10 11 95 95 31 39 99 31 91 9 44 95 8 17 8 73 50 80 29 94 17 45 7 67 71 55 13 66 46 72 100 83 97 77 86 29 55 55 62 2 2 62 76 78 85 58 19 90 44 2 89 5 39 20 86 7 98 27 75 81 44 89 19 5 26 64 79 24 42 43 4 62 53 35 42 52 42 47 57 2 13 11 54 77 99 91 27 78 40 25 55 57 45 84 4 35 55 24 1 80 97 92 53 55 97 95 43 99 71 83 7 89 9 78 10 62 43 35 20 22 35 43 94 32 1 74 44 53 47 59 45 82 67 84 47 8 91 76 54 77 66 48 10 12 78 72 39 76 50 57 90 46 57 42 77 25 94 6 26 80 77 12 15 47 27 74 90 45 37 62 86 66 96 22 85 61 2 90 19 55 100 18 7 54 7 43 19 42 64 30 5 78 71 61 95 48 71 46 1 53 43 53 90 63 83 13 92 100 84 19 79 51 88 99 19 95 44 24 10 92 19 43 79 62 50 74 48 54 88 77 90 57 27 39 5 73 60 98 32 73 64 22 35 16 6 2 9 8 90 28 98 28 94 90 94 86 76 60 73 86 90 74 99 23 59 40 58 57 86 26 72 76 68 97 74 83 91 5 52 55 28 93 5 87 77 30 24 17 59 29 96 33 71 72 47 93 68 52 50 16 15 88 95 88 53 56 74 35 83 13 71 11 76 6 30 20 59 93 84 38 24 67 31 14 80 87 31 86 58 83 43 79 3 85 24 48 29 47 54 45 55 31 18 74 97 33 28 46 5 56 8 41 5 41 87 83 51 57 38 72 70 49 87 15 71 13 71 82 68 6 73 56 63 51 38 69 55 54 97 23 82 15 36 74 15 19 10 43 74 72 5 36 97 88 53 68 87 80 38 97 30 94 56 28 61 11 16 89 31 13 2 63 41 36 57 53 90 64 32 9 40 48 54 71 85 20 100 81 42 34 8 10 52 33 66 36 87 66 79 25 84 39 35 66 35 35 61 16 47 27 31 97 20 76 90 33 37 58 37 48 6 12 50 31 19 48 13 8 78 69 26 82 45 74 2 12 71 47 14 73 46 61 4 38 51 99 37 100 34 98 49 14 34 98 3 90 92 19 75 27 12 59 14 87 63 22 9 76 9 67 23 76 65 14 17 71 27 37 51 94 36 77 87 25 38 68 98 34 9 90 94 79 46 5 7 22 95 97 86 72 74 40 40 100 24 29 29 66 11 62 84 31 47 35 30 61 67 61 90 20 26 8 12 93 95 42 31 50 42 61 31 5 75 53 7 99 95 1 21 22 72 51 14 46 92 92 15 48 36 44 16 19 41 25 65 66 98 47 78 44 63 81 34 88 6 52 93 38 67 20 21 88 67 82 38 38 25 31 99 51 93 91 78 11 77 46 31 45 44 9 35 4 69 5 22 33 42 90 90 58 29 31 53 34 23 7 34 100 73 15 79 31 61 92 89 3 26 47 14 94 92 35 13 54 99 91 99
样例输出
6822 28476 4578 261 339042 289447 117476 29 537693 88998 8640 2480 2810 1001 27117 39377 2 191862 6656 85122 58662 68006 137300 121860 34502 58674 2 120050 131810 137747 93 451215 3438 52992 386100 124700 7232 60760 13708 22563 160 7126 4472 272288 63552 33120 578 234192 2 236236 143312 77300 163202 39899 91982 32064 104834 244380 2598 61217 98238 369371 58975 970 23150 320418 2502 9826 2732 167915 548 234842 5370 222 7562 190077 21298 40419 6188 100113 56112 24192 100821 8588 80660 46562 42282 92796 1818 576 2816 23837 1077 86034 258479 62370 56608 14724 102 439022 644 195170 43526 368 5792 350948 520847 8309 23375 416772 22518 2758 218405 2 10127 20412 151268 89780 147864 74178 12512 420626 8672 71892 116522 14586 34550 163302 765947 10220 412742 413 3762 266240 18293 338 48372 181400 85871 16332 98482 309 4123 9146 860 4257 179114 37816 9375 91466 88767 316640 870865 271593 246502 762 83722 457418 191648 498902 169150 10832 38752 41327 97377 723668 11837 30153 62560 4314 306466 41258 322371 28550 277452 16 169677 48860 8372 380562 15642 41728 103077 3918 5027 42704 104834 129816 75040 48 488 157898 87 3762 420626 68991 284 321882 39587 63804 66594 43362 2 62 6752 53363 19800 3146 171794 21465 124830 120230 24336 9037 584 369172 90650 204741 581339 17937 64049 488550 17503 10752 206741 96 283774 445813 12276 4477 172227 2 121187 2144 50085 18090 7982 9037 71840 187514 11666 510 6392 252063 350 30240 81588 1632 246 4550 314096 32564 41002 181400 61355 19550 12752 2466 29538 261828 2332 241110 233760 61346 40770 128725 17160 331784 8312 51648 103870 61778 326720 380347 310248 110292 1892 116910 26840 89 64820 684777 34452 364949 18293 51 178950 37004 28652 324610 896 487502 18506 27027 744218 300830 428510 114024 22840 118536 22167 158576 393785 7904 116012 2730 55397 318656 6294 291092 14450 4710 972 100122 119117 256322 238812 198476 3762 470122 918 987 1227 2540 21576 1280 150308 3068 328736 16254 1463 3542 26609 2664 95684 69 2730 111153 7826 111768 322371 59117 89357 30287 23922 5852 1227 3918 130895 24068 85293 123797 128725 16676 267687 12443 46688 954 86 32697 6671 58425 14322 464 404858 2502 6656 2 2662 236 50808 6125 153596 115702 57045 2717 299650 54932 17600 15948 29889 283010 1740 2592 8216 14214 156572 70 411660 113242 134138 186452 45885 10982 324704 69632 108 2 165 3654 2 131582 12432 11358 102582 20834 2261 318 53632 270537 4125 39587 2167 120050 107113 1694 67305 80 23352 258540 602 7992 1696 51732 15810 9492 42282 5408 2 4472 127106 70632 20834 16056 92648 20033 508523 254678 2180 1460 244380 272700 76342 800 216659 183372 20286 8910 48875 103202 19362 93150 576 69 38082 1883 338 55 157682 119763 834396 79205 107732 553160 414216 5018 3102 8325 64022 3330 212465 47475 8930 70818 597944 187514 70670 3935 141218 6615 332930 475524 3577 61355 2 322530 8588 148616 139077 48 80082 20387 302 24350 1415 22682 318 29750 106697 30674 10287 2070 29304 91982 381710 95804 307463 382832 56175 92648 2180 1589 122247 10234 173734 2 41327 42 498902 4335 462462 99920 126571 2051 39248 159477 210786 236322 7581 235530 133977 4745 351912 121991 57722 6888 44660 51212 14722 458025 242706 59922 234525 98 1638 1152 41820 50754 191634 6512 1332 2004 6492 917426 444752 78435 1998 990 18506 500 1497 19019 102 11672 507 340 1799 14676 77 226746 4532 118041 360527 269160 1595 106020 19 1362 8145 118379 49184 21320 45167 17750 40068 33996 1040 33852 352038 186136 657050 39366 46097 31808 6032 1169 42690 82 220 81588 554738 111960 88580 7826 28406 86034 596 4032 3720 4587 244380 121860 256331 624920 3692 460 246150 304794 14042 139968 90 231990 359076 1392 1152 88652 30 546840 55862 51648 33320 486642 63461 276320 320 677295 464720 57090 98472 1302 76932 578018 3096 642 250686 2717 15810 173810 55740 7380 2796 149450 226577 639200 292922 238148 288 6032 27050 736386 724638 5490 496199 75998 22404 611228 413 5962 59582 103818 57722 1998 2956 772 153225 45124 15402 1148 309674 5486 118082 444888 619512 482944 34974 176825 10 264864 495651 13547 128744 97 470 20560 2261 36558 120230 18848 340 292448 18816 302 161332 47075 82740 114680 21 3707 520982 42174 93680 24650 103050 548 54810 2 565800 202672 228800 126506 427562 1946 3618 4070 96707 10870 13673 125603 2 113608 110356 105030 333995 143867 2844 189000 311157 2720 6096 83811 156900 237918 108767 104265 36350 522 465388 1938 26730 448514 56018 283774 351912 25223 69 19019 233255 581 1337 10982 93072 380 375377 289262 136584 2 88580 199916 289170 8372 648564 17138 179877 20558 133474 1640 19361 112058 139750 139968 206172 494648 30240 470 239070 65536 280352 13673 372 17 2816 48440 46928 745110 467552 239070 650762 472823 21298 78080 231534 32552 332724 467421 599094 600 32186 1010 485870 15504 10642 51620 56034 130895 371450 127500 3495 708356 197160 203392 71470 6734 4917 582 15430 624162 17712 46562 8764 55862 241454 115670 258 30684 32132 111437 101070 7839 467421 23870 540 1864 490 106682 173502 68267 347900 162386 9270 6734 346392 1227 186452 64049 187220 219051 27117 5595 9585 1415 107543 800 85122 197160 357782 84436 56175 234192 34454 1617 56792 21 87002 59922 199916 48672 1854 117408 392772 23220 107709 1248 2900 53394 78822 315447 33350 45290 61355 58380 7832 21114 22650 478952 38082 64676 852 4248 8930 4940 2480 31577 127800 82 5634 5761 125327 410 64049 91982 76364 175322 4578 315 737100 16454 2730 6853 296982 1206 3150 23322 297570 3031 35154 60014 83232 485870 19550 382840 1638 745110 131537 150 27533 676347 378432 64040 34824 24418 4367 279992 37262 29205 238022 280112 9160 632 813006 34937 81018 43772 830 1316 875330 2 22220 6125 144992 11475 54252 7472 10640 27650 356202 137381 103202 65705 1452 195026 75297 8210 347261 85842 19550 61442 186252 513669 4972 36797 86174 1674 458 300 40722 729090 36192 40052 14973 917 460046 10110 43772 716806 99 5761 787152 3926 221913 786422