P19132 [HackerEarth] Roy has a number of coins with him that he loves playing with by arranging them in the form of N stacks numbered sequentially. Lucy now gives him a task to make his arrangement of coins
普及
题目描述

Roy has a number of coins with him that he loves playing with by arranging them in the form of N stacks numbered sequentially. Lucy now gives him a task to make his arrangement of coins even more interesting. The arrangement will be interesting if the number of coins in the stacks are in strictly increasing order.

For this task Lucy gives Roy the option to modify his arrangement by increasing or decreasing the number of coins in each of the stack by atmost C coins. Also the number of coins in a stack should not fall below 1.

Your mission, should you choose to accept it, is to report the minimum C that helps Roy complete the assigned task.

Input
First line contains T, the number of test cases

Each test case contains two lines. The first line has a single integer N. The second line contains N space separated integers denoting the number of coins in the stacks initially.

Output
A single line for each test case containing the answer as explained in the statement.

Constraints
1 ≤ T ≤ 200
2 ≤ N ≤ 1000
The number of coins initially in each of the stack is between 1 and 1000000000.

SAMPLE INPUT
2
3
9 5 3
5
2 2 2 2 2

SAMPLE OUTPUT
4
3

输入格式

见题面

输出格式

见题面

样例输入
189 3 9 5 11 2 5 8 5 1 1 1 1 1 5 548 47 58 250 2012 2 1 1 2 2 2 2 2 1 2 1 1 4 8 5 100 90 5 5 4 3 2 1 4 548 7 2 2012 2 1000000000 1000000000 50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 50 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 50 1 999999999 2 999999998 3 999999997 4 999999996 5 999999995 6 999999994 7 999999993 8 999999992 9 999999991 10 999999990 11 999999989 12 999999988 13 999999987 14 999999986 15 999999985 16 999999984 17 999999983 18 999999982 19 999999981 20 999999980 21 999999979 22 999999978 23 999999977 24 999999976 25 999999975 50 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 49 654914335 770745116 950029501 116648027 602800923 742336129 976019296 870244936 183567425 553245339 599783804 355942031 609224485 914303931 322713429 698460259 952212914 436949547 106066931 217367893 213218886 32083533 813721427 54811269 281854248 117721910 651592383 566763127 434294918 191486567 854490778 89209252 962231682 804520278 58373630 565032604 399372758 886909278 287793891 435456534 292670968 740094047 791398565 901895452 654397977 114111993 452872063 459127242 403577891 43 676495135 616796776 443538877 342732913 524124397 577909476 312971174 175716779 144672603 747266091 367203345 851679732 688991694 181951379 508716361 599881676 746983982 908089119 486790953 887294225 196062004 779461920 627388271 987460568 533873724 134302599 954088912 986745786 445946192 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2 36 1000000000 1 499999999 15922 12 124124 9999 1 124124124 124124 112312 12344 46456 78678 1 1 1 1 1 436456 1 1 1 1 56457 666 888 33334 234 124 12 1 2 232332 24421 124 7 2 2 2 2 2 2 2 3 3 2 1 3 3 3 4 4 10 5 5 1 50 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 2 1000000000 6 5 4 5 8 9 8 3 2 4 3 9 3 3 3 3 3 3 3 3 1 3 100 70 1 50 201629285 54181223 90731827 216410213 516618714 327303149 71367048 608557413 707296471 2763724 791209384 637357858 425071364 643788020 915600326 419826452 539381563 650417126 661835224 292280080 56187065 236158547 566902967 700691471 514194721 596463513 308581989 164464812 348624789 1422901 85338762 562458510 17146670 421257186 963407784 760889080 145116516 17801770 487083229 993129211 279727987 339535998 510430079 394129760 299292166 589694460 150720087 62244168 899135837 726550292 3 1 2 2 37 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1 1 2 1 2 1 2 2 2 2 1 2 1 50 1000000000 999999900 999999800 999999700 999999600 999999500 999999400 999999300 999999200 999999100 999999000 999998900 999998800 999998700 999998600 999998500 999998400 999998300 999998200 999998100 999998000 999997900 999997800 999997700 999997600 999997500 999997400 999997300 999997200 999997100 999997000 999996900 999996800 999996700 999996600 999996500 999996400 999996300 999996200 999996100 999996000 999995900 999995800 999995700 999995600 999995500 999995400 999995300 999995200 1 50 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 4 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2 2 2 8 4 3 2 1 6 5 4 3 5 1 1 1 1 1 50 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 17 5 5 3 1 2 3 2 1 1 2 1 2 4 6 5 3 4 3 4 4 1 9 2 3 4 5 6 7 8 9 9 3 4 2 1 5 11 11 11 11 11 3 100000016 100000008 100000000 2 1 14 4 9 5 10 5 11 1 2 3 4 5 6 7 8 9 10 5 48 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 100000000 1 1000000000 1 100000000 1 100000000 1 100000000 1 100000000 1 100000000 1 100000000 1 100000000 1 3 1 1 2 4 1 4900 5000 100 29 1 100000000 1 100000000 1 100000000 1 1 1 1 1 1 1 100000000 100000000 1 1 100000000 100000000 100000000 100000000 100000000 1 1 1 1 100000000 100000000 1 3 9 5 11 4 1 2 100 3 11 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
样例输出
482494 453072 441757 452782 458133 491719 464273 468536 454903 455699 455129 477143 463979 476913 457307 473683 470316 457431 448049 481800 458185 439288 449107 461479 468820 465071 473592 470160 483690 479014 471203 454425 471167 465390 480673 454819 463175 476316 467366 467078 457775 446790 459409 445763 455999 474873 453685 458208 477649 474780 478696 460785 490696 460095 468352 459701 453542 454196 450866 472268 450862 462789 455016 462884 494249 445397 439315 459280 465653 463491 471758 457657 425929 474199 471170 476267 467274 446435 438902 455722 466106 468283 452778 452436 474543 470026 474385 449911 470721 467307 461828 443710 475540 466888 440763 444527 464567 446772 467515 470083 479382 461372 483138 428408 448122 448522 451675 477381 474231 478337 445125 450952 463535 481920 456937 468906 449098 473950 473605 449169 457306 445621 473522 465096 468283 466614 447036 460411 469422 483106 467620 464751 477762 471749 472458 458889 444136 445781 466399 456166 443486 446853 458965 464409 477495 451593 477133 453461 470896 467928 462278 452616 486625 463653 457145 465468 484902 466396 473208 471713 436490 462572 471972 435996 460176 483530 463469 444125 451441 477960 473101 447381 477253 466298 467626 459439 458497 450713 445012 454215 482273 464504 458494 469351 452626 452957 457887 444191 463623 457934 474263 444845 473349 457886 455583 467096 447926 466735 468989 459235