// primef.h
static int np = 1000000; 
static long int primes[]={ 
2l, 
3l, 5l, 7l, 11l, 13l, 17l, 19l, 
23l, 29l, 31l, 37l, 41l, 43l, 47l, 
53l, 59l, 61l, 67l, 71l, 73l, 79l, 
83l, 89l, 97l, 101l, 103l, 107l, 109l, 
113l, 127l, 131l, 137l, 139l, 149l, 151l, 
157l, 163l, 167l, 173l, 179l, 181l, 191l, 
193l, 197l, 199l, 211l, 223l, 227l, 229l, 
233l, 239l, 241l, 251l, 257l, 263l, 269l, 
271l, 277l, 281l, 283l, 293l, 307l, 311l, 
313l, 317l, 331l, 337l, 347l, 349l, 353l, 
359l, 367l, 373l, 379l, 383l, 389l, 397l, 
401l, 409l, 419l, 421l, 431l, 433l, 439l, 
443l, 449l, 457l, 461l, 463l, 467l, 479l, 
487l, 491l, 499l, 503l, 509l, 521l, 523l, 
541l, 547l, 557l, 563l, 569l, 571l, 577l, 
587l, 593l, 599l, 601l, 607l, 613l, 617l, 
619l, 631l, 641l, 643l, 647l, 653l, 659l, 
661l, 673l, 677l, 683l, 691l, 701l, 709l, 
719l, 727l, 733l, 739l, 743l, 751l, 757l, 
761l, 769l, 773l, 787l, 797l, 809l, 811l, 
821l, 823l, 827l, 829l, 839l, 853l, 857l, 
859l, 863l, 877l, 881l, 883l, 887l, 907l, 
911l, 919l, 929l, 937l, 941l, 947l, 953l, 
967l, 971l, 977l, 983l, 991l, 997l, 1009l, 
1013l, 1019l, 1021l, 1031l, 1033l, 1039l, 1049l, 
1051l, 1061l, 1063l, 1069l, 1087l, 1091l, 1093l, 
1097l, 1103l, 1109l, 1117l, 1123l, 1129l, 1151l, 
1153l, 1163l, 1171l, 1181l, 1187l, 1193l, 1201l, 
1213l, 1217l, 1223l, 1229l, 1231l, 1237l, 1249l, 
1259l, 1277l, 1279l, 1283l, 1289l, 1291l, 1297l, 
1301l, 1303l, 1307l, 1319l, 1321l, 1327l, 1361l, 
1367l, 1373l, 1381l, 1399l, 1409l, 1423l, 1427l, 
1429l, 1433l, 1439l, 1447l, 1451l, 1453l, 1459l, 
1471l, 1481l, 1483l, 1487l, 1489l, 1493l, 1499l, 
1511l, 1523l, 1531l, 1543l, 1549l, 1553l, 1559l, 
1567l, 1571l, 1579l, 1583l, 1597l, 1601l, 1607l, 
1609l, 1613l, 1619l, 1621l, 1627l, 1637l, 1657l, 
1663l, 1667l, 1669l, 1693l, 1697l, 1699l, 1709l, 
1721l, 1723l, 1733l, 1741l, 1747l, 1753l, 1759l, 
1777l, 1783l, 1787l, 1789l, 1801l, 1811l, 1823l, 
1831l, 1847l, 1861l, 1867l, 1871l, 1873l, 1877l, 
1879l, 1889l, 1901l, 1907l, 1913l, 1931l, 1933l, 
1949l, 1951l, 1973l, 1979l, 1987l, 1993l, 1997l, 
1999l, 2003l, 2011l, 2017l, 2027l, 2029l, 2039l, 
2053l, 2063l, 2069l, 2081l, 2083l, 2087l, 2089l, 
2099l, 2111l, 2113l, 2129l, 2131l, 2137l, 2141l, 
2143l, 2153l, 2161l, 2179l, 2203l, 2207l, 2213l, 
2221l, 2237l, 2239l, 2243l, 2251l, 2267l, 2269l, 
2273l, 2281l, 2287l, 2293l, 2297l, 2309l, 2311l, 
2333l, 2339l, 2341l, 2347l, 2351l, 2357l, 2371l, 
2377l, 2381l, 2383l, 2389l, 2393l, 2399l, 2411l, 
2417l, 2423l, 2437l, 2441l, 2447l, 2459l, 2467l, 
2473l, 2477l, 2503l, 2521l, 2531l, 2539l, 2543l, 
2549l, 2551l, 2557l, 2579l, 2591l, 2593l, 2609l, 
2617l, 2621l, 2633l, 2647l, 2657l, 2659l, 2663l, 
2671l, 2677l, 2683l, 2687l, 2689l, 2693l, 2699l, 
2707l, 2711l, 2713l, 2719l, 2729l, 2731l, 2741l, 
2749l, 2753l, 2767l, 2777l, 2789l, 2791l, 2797l, 
2801l, 2803l, 2819l, 2833l, 2837l, 2843l, 2851l, 
2857l, 2861l, 2879l, 2887l, 2897l, 2903l, 2909l, 
2917l, 2927l, 2939l, 2953l, 2957l, 2963l, 2969l, 
2971l, 2999l, 3001l, 3011l, 3019l, 3023l, 3037l, 
3041l, 3049l, 3061l, 3067l, 3079l, 3083l, 3089l, 
3109l, 3119l, 3121l, 3137l, 3163l, 3167l, 3169l, 
3181l, 3187l, 3191l, 3203l, 3209l, 3217l, 3221l, 
3229l, 3251l, 3253l, 3257l, 3259l, 3271l, 3299l, 
3301l, 3307l, 3313l, 3319l, 3323l, 3329l, 3331l, 
3343l, 3347l, 3359l, 3361l, 3371l, 3373l, 3389l, 
3391l, 3407l, 3413l, 3433l, 3449l, 3457l, 3461l, 
3463l, 3467l, 3469l, 3491l, 3499l, 3511l, 3517l, 
3527l, 3529l, 3533l, 3539l, 3541l, 3547l, 3557l, 
3559l, 3571l, 3581l, 3583l, 3593l, 3607l, 3613l, 
3617l, 3623l, 3631l, 3637l, 3643l, 3659l, 3671l, 
3673l, 3677l, 3691l, 3697l, 3701l, 3709l, 3719l, 
3727l, 3733l, 3739l, 3761l, 3767l, 3769l, 3779l, 
3793l, 3797l, 3803l, 3821l, 3823l, 3833l, 3847l, 
3851l, 3853l, 3863l, 3877l, 3881l, 3889l, 3907l, 
3911l, 3917l, 3919l, 3923l, 3929l, 3931l, 3943l, 
3947l, 3967l, 3989l, 4001l, 4003l, 4007l, 4013l, 
4019l, 4021l, 4027l, 4049l, 4051l, 4057l, 4073l, 
4079l, 4091l, 4093l, 4099l, 4111l, 4127l, 4129l, 
4133l, 4139l, 4153l, 4157l, 4159l, 4177l, 4201l, 
4211l, 4217l, 4219l, 4229l, 4231l, 4241l, 4243l, 
4253l, 4259l, 4261l, 4271l, 4273l, 4283l, 4289l, 
4297l, 4327l, 4337l, 4339l, 4349l, 4357l, 4363l, 
4373l, 4391l, 4397l, 4409l, 4421l, 4423l, 4441l, 
4447l, 4451l, 4457l, 4463l, 4481l, 4483l, 4493l, 
4507l, 4513l, 4517l, 4519l, 4523l, 4547l, 4549l, 
4561l, 4567l, 4583l, 4591l, 4597l, 4603l, 4621l, 
4637l, 4639l, 4643l, 4649l, 4651l, 4657l, 4663l, 
4673l, 4679l, 4691l, 4703l, 4721l, 4723l, 4729l, 
4733l, 4751l, 4759l, 4783l, 4787l, 4789l, 4793l, 
4799l, 4801l, 4813l, 4817l, 4831l, 4861l, 4871l, 
4877l, 4889l, 4903l, 4909l, 4919l, 4931l, 4933l, 
4937l, 4943l, 4951l, 4957l, 4967l, 4969l, 4973l, 
4987l, 4993l, 4999l, 5003l, 5009l, 5011l, 5021l, 
5023l, 5039l, 5051l, 5059l, 5077l, 5081l, 5087l, 
5099l, 5101l, 5107l, 5113l, 5119l, 5147l, 5153l, 
5167l, 5171l, 5179l, 5189l, 5197l, 5209l, 5227l, 
5231l, 5233l, 5237l, 5261l, 5273l, 5279l, 5281l, 
5297l, 5303l, 5309l, 5323l, 5333l, 5347l, 5351l, 
5381l, 5387l, 5393l, 5399l, 5407l, 5413l, 5417l, 
5419l, 5431l, 5437l, 5441l, 5443l, 5449l, 5471l, 
5477l, 5479l, 5483l, 5501l, 5503l, 5507l, 5519l, 
5521l, 5527l, 5531l, 5557l, 5563l, 5569l, 5573l, 
5581l, 5591l, 5623l, 5639l, 5641l, 5647l, 5651l, 
5653l, 5657l, 5659l, 5669l, 5683l, 5689l, 5693l, 
5701l, 5711l, 5717l, 5737l, 5741l, 5743l, 5749l, 
5779l, 5783l, 5791l, 5801l, 5807l, 5813l, 5821l, 
5827l, 5839l, 5843l, 5849l, 5851l, 5857l, 5861l, 
5867l, 5869l, 5879l, 5881l, 5897l, 5903l, 5923l, 
5927l, 5939l, 5953l, 5981l, 5987l, 6007l, 6011l, 
6029l, 6037l, 6043l, 6047l, 6053l, 6067l, 6073l, 
6079l, 6089l, 6091l, 6101l, 6113l, 6121l, 6131l, 
6133l, 6143l, 6151l, 6163l, 6173l, 6197l, 6199l, 
6203l, 6211l, 6217l, 6221l, 6229l, 6247l, 6257l, 
6263l, 6269l, 6271l, 6277l, 6287l, 6299l, 6301l, 
6311l, 6317l, 6323l, 6329l, 6337l, 6343l, 6353l, 
6359l, 6361l, 6367l, 6373l, 6379l, 6389l, 6397l, 
6421l, 6427l, 6449l, 6451l, 6469l, 6473l, 6481l, 
6491l, 6521l, 6529l, 6547l, 6551l, 6553l, 6563l, 
6569l, 6571l, 6577l, 6581l, 6599l, 6607l, 6619l, 
6637l, 6653l, 6659l, 6661l, 6673l, 6679l, 6689l, 
6691l, 6701l, 6703l, 6709l, 6719l, 6733l, 6737l, 
6761l, 6763l, 6779l, 6781l, 6791l, 6793l, 6803l, 
6823l, 6827l, 6829l, 6833l, 6841l, 6857l, 6863l, 
6869l, 6871l, 6883l, 6899l, 6907l, 6911l, 6917l, 
6947l, 6949l, 6959l, 6961l, 6967l, 6971l, 6977l, 
6983l, 6991l, 6997l, 7001l, 7013l, 7019l, 7027l, 
7039l, 7043l, 7057l, 7069l, 7079l, 7103l, 7109l, 
7121l, 7127l, 7129l, 7151l, 7159l, 7177l, 7187l, 
7193l, 7207l, 7211l, 7213l, 7219l, 7229l, 7237l, 
7243l, 7247l, 7253l, 7283l, 7297l, 7307l, 7309l, 
7321l, 7331l, 7333l, 7349l, 7351l, 7369l, 7393l, 
7411l, 7417l, 7433l, 7451l, 7457l, 7459l, 7477l, 
7481l, 7487l, 7489l, 7499l, 7507l, 7517l, 7523l, 
7529l, 7537l, 7541l, 7547l, 7549l, 7559l, 7561l, 
7573l, 7577l, 7583l, 7589l, 7591l, 7603l, 7607l, 
7621l, 7639l, 7643l, 7649l, 7669l, 7673l, 7681l, 
7687l, 7691l, 7699l, 7703l, 7717l, 7723l, 7727l, 
7741l, 7753l, 7757l, 7759l, 7789l, 7793l, 7817l, 
7823l, 7829l, 7841l, 7853l, 7867l, 7873l, 7877l, 
7879l, 7883l, 7901l, 7907l, 7919l, 7927l, 7933l, 
7937l, 7949l, 7951l, 7963l, 7993l, 8009l, 8011l, 
8017l, 8039l, 8053l, 8059l, 8069l, 8081l, 8087l, 
8089l, 8093l, 8101l, 8111l, 8117l, 8123l, 8147l, 
8161l, 8167l, 8171l, 8179l, 8191l, 8209l, 8219l, 
8221l, 8231l, 8233l, 8237l, 8243l, 8263l, 8269l, 
8273l, 8287l, 8291l, 8293l, 8297l, 8311l, 8317l, 
8329l, 8353l, 8363l, 8369l, 8377l, 8387l, 8389l, 
8419l, 8423l, 8429l, 8431l, 8443l, 8447l, 8461l, 
8467l, 8501l, 8513l, 8521l, 8527l, 8537l, 8539l, 
8543l, 8563l, 8573l, 8581l, 8597l, 8599l, 8609l, 
8623l, 8627l, 8629l, 8641l, 8647l, 8663l, 8669l, 
8677l, 8681l, 8689l, 8693l, 8699l, 8707l, 8713l, 
8719l, 8731l, 8737l, 8741l, 8747l, 8753l, 8761l, 
8779l, 8783l, 8803l, 8807l, 8819l, 8821l, 8831l, 
8837l, 8839l, 8849l, 8861l, 8863l, 8867l, 8887l, 
8893l, 8923l, 8929l, 8933l, 8941l, 8951l, 8963l, 
8969l, 8971l, 8999l, 9001l, 9007l, 9011l, 9013l, 
9029l, 9041l, 9043l, 9049l, 9059l, 9067l, 9091l, 
9103l, 9109l, 9127l, 9133l, 9137l, 9151l, 9157l, 
9161l, 9173l, 9181l, 9187l, 9199l, 9203l, 9209l, 
9221l, 9227l, 9239l, 9241l, 9257l, 9277l, 9281l, 
9283l, 9293l, 9311l, 9319l, 9323l, 9337l, 9341l, 
9343l, 9349l, 9371l, 9377l, 9391l, 9397l, 9403l, 
9413l, 9419l, 9421l, 9431l, 9433l, 9437l, 9439l, 
9461l, 9463l, 9467l, 9473l, 9479l, 9491l, 9497l, 
9511l, 9521l, 9533l, 9539l, 9547l, 9551l, 9587l, 
9601l, 9613l, 9619l, 9623l, 9629l, 9631l, 9643l, 
9649l, 9661l, 9677l, 9679l, 9689l, 9697l, 9719l, 
9721l, 9733l, 9739l, 9743l, 9749l, 9767l, 9769l, 
9781l, 9787l, 9791l, 9803l, 9811l, 9817l, 9829l, 
9833l, 9839l, 9851l, 9857l, 9859l, 9871l, 9883l, 
9887l, 9901l, 9907l, 9923l, 9929l, 9931l, 9941l, 
9949l, 9967l, 9973l, 10007l, 10009l, 10037l, 10039l, 
10061l, 10067l, 10069l, 10079l, 10091l, 10093l, 10099l, 
10103l, 10111l, 10133l, 10139l, 10141l, 10151l, 10159l, 
10163l, 10169l, 10177l, 10181l, 10193l, 10211l, 10223l, 
10243l, 10247l, 10253l, 10259l, 10267l, 10271l, 10273l, 
10289l, 10301l, 10303l, 10313l, 10321l, 10331l, 10333l, 
10337l, 10343l, 10357l, 10369l, 10391l, 10399l, 10427l, 
10429l, 10433l, 10453l, 10457l, 10459l, 10463l, 10477l, 
10487l, 10499l, 10501l, 10513l, 10529l, 10531l, 10559l, 
10567l, 10589l, 10597l, 10601l, 10607l, 10613l, 10627l, 
10631l, 10639l, 10651l, 10657l, 10663l, 10667l, 10687l, 
10691l, 10709l, 10711l, 10723l, 10729l, 10733l, 10739l, 
10753l, 10771l, 10781l, 10789l, 10799l, 10831l, 10837l, 
10847l, 10853l, 10859l, 10861l, 10867l, 10883l, 10889l, 
10891l, 10903l, 10909l, 10937l, 10939l, 10949l, 10957l, 
10973l, 10979l, 10987l, 10993l, 11003l, 11027l, 11047l, 
11057l, 11059l, 11069l, 11071l, 11083l, 11087l, 11093l, 
11113l, 11117l, 11119l, 11131l, 11149l, 11159l, 11161l, 
11171l, 11173l, 11177l, 11197l, 11213l, 11239l, 11243l, 
11251l, 11257l, 11261l, 11273l, 11279l, 11287l, 11299l, 
11311l, 11317l, 11321l, 11329l, 11351l, 11353l, 11369l, 
11383l, 11393l, 11399l, 11411l, 11423l, 11437l, 11443l, 
11447l, 11467l, 11471l, 11483l, 11489l, 11491l, 11497l, 
11503l, 11519l, 11527l, 11549l, 11551l, 11579l, 11587l, 
11593l, 11597l, 11617l, 11621l, 11633l, 11657l, 11677l, 
11681l, 11689l, 11699l, 11701l, 11717l, 11719l, 11731l, 
11743l, 11777l, 11779l, 11783l, 11789l, 11801l, 11807l, 
11813l, 11821l, 11827l, 11831l, 11833l, 11839l, 11863l, 
11867l, 11887l, 11897l, 11903l, 11909l, 11923l, 11927l, 
11933l, 11939l, 11941l, 11953l, 11959l, 11969l, 11971l, 
11981l, 11987l, 12007l, 12011l, 12037l, 12041l, 12043l, 
12049l, 12071l, 12073l, 12097l, 12101l, 12107l, 12109l, 
12113l, 12119l, 12143l, 12149l, 12157l, 12161l, 12163l, 
12197l, 12203l, 12211l, 12227l, 12239l, 12241l, 12251l, 
12253l, 12263l, 12269l, 12277l, 12281l, 12289l, 12301l, 
12323l, 12329l, 12343l, 12347l, 12373l, 12377l, 12379l, 
12391l, 12401l, 12409l, 12413l, 12421l, 12433l, 12437l, 
12451l, 12457l, 12473l, 12479l, 12487l, 12491l, 12497l, 
12503l, 12511l, 12517l, 12527l, 12539l, 12541l, 12547l, 
12553l, 12569l, 12577l, 12583l, 12589l, 12601l, 12611l, 
12613l, 12619l, 12637l, 12641l, 12647l, 12653l, 12659l, 
12671l, 12689l, 12697l, 12703l, 12713l, 12721l, 12739l, 
12743l, 12757l, 12763l, 12781l, 12791l, 12799l, 12809l, 
12821l, 12823l, 12829l, 12841l, 12853l, 12889l, 12893l, 
12899l, 12907l, 12911l, 12917l, 12919l, 12923l, 12941l, 
12953l, 12959l, 12967l, 12973l, 12979l, 12983l, 13001l, 
13003l, 13007l, 13009l, 13033l, 13037l, 13043l, 13049l, 
13063l, 13093l, 13099l, 13103l, 13109l, 13121l, 13127l, 
13147l, 13151l, 13159l, 13163l, 13171l, 13177l, 13183l, 
13187l, 13217l, 13219l, 13229l, 13241l, 13249l, 13259l, 
13267l, 13291l, 13297l, 13309l, 13313l, 13327l, 13331l, 
13337l, 13339l, 13367l, 13381l, 13397l, 13399l, 13411l, 
13417l, 13421l, 13441l, 13451l, 13457l, 13463l, 13469l, 
13477l, 13487l, 13499l, 13513l, 13523l, 13537l, 13553l, 
13567l, 13577l, 13591l, 13597l, 13613l, 13619l, 13627l, 
13633l, 13649l, 13669l, 13679l, 13681l, 13687l, 13691l, 
13693l, 13697l, 13709l, 13711l, 13721l, 13723l, 13729l, 
13751l, 13757l, 13759l, 13763l, 13781l, 13789l, 13799l, 
13807l, 13829l, 13831l, 13841l, 13859l, 13873l, 13877l, 
13879l, 13883l, 13901l, 13903l, 13907l, 13913l, 13921l, 
13931l, 13933l, 13963l, 13967l, 13997l, 13999l, 14009l, 
14011l, 14029l, 14033l, 14051l, 14057l, 14071l, 14081l, 
14083l, 14087l, 14107l, 14143l, 14149l, 14153l, 14159l, 
14173l, 14177l, 14197l, 14207l, 14221l, 14243l, 14249l, 
14251l, 14281l, 14293l, 14303l, 14321l, 14323l, 14327l, 
14341l, 14347l, 14369l, 14387l, 14389l, 14401l, 14407l, 
14411l, 14419l, 14423l, 14431l, 14437l, 14447l, 14449l, 
14461l, 14479l, 14489l, 14503l, 14519l, 14533l, 14537l, 
14543l, 14549l, 14551l, 14557l, 14561l, 14563l, 14591l, 
14593l, 14621l, 14627l, 14629l, 14633l, 14639l, 14653l, 
14657l, 14669l, 14683l, 14699l, 14713l, 14717l, 14723l, 
14731l, 14737l, 14741l, 14747l, 14753l, 14759l, 14767l, 
14771l, 14779l, 14783l, 14797l, 14813l, 14821l, 14827l, 
14831l, 14843l, 14851l, 14867l, 14869l, 14879l, 14887l, 
14891l, 14897l, 14923l, 14929l, 14939l, 14947l, 14951l, 
14957l, 14969l, 14983l, 15013l, 15017l, 15031l, 15053l, 
15061l, 15073l, 15077l, 15083l, 15091l, 15101l, 15107l, 
15121l, 15131l, 15137l, 15139l, 15149l, 15161l, 15173l, 
15187l, 15193l, 15199l, 15217l, 15227l, 15233l, 15241l, 
15259l, 15263l, 15269l, 15271l, 15277l, 15287l, 15289l, 
15299l, 15307l, 15313l, 15319l, 15329l, 15331l, 15349l, 
15359l, 15361l, 15373l, 15377l, 15383l, 15391l, 15401l, 
15413l, 15427l, 15439l, 15443l, 15451l, 15461l, 15467l, 
15473l, 15493l, 15497l, 15511l, 15527l, 15541l, 15551l, 
15559l, 15569l, 15581l, 15583l, 15601l, 15607l, 15619l, 
15629l, 15641l, 15643l, 15647l, 15649l, 15661l, 15667l, 
15671l, 15679l, 15683l, 15727l, 15731l, 15733l, 15737l, 
15739l, 15749l, 15761l, 15767l, 15773l, 15787l, 15791l, 
15797l, 15803l, 15809l, 15817l, 15823l, 15859l, 15877l, 
15881l, 15887l, 15889l, 15901l, 15907l, 15913l, 15919l, 
15923l, 15937l, 15959l, 15971l, 15973l, 15991l, 16001l, 
16007l, 16033l, 16057l, 16061l, 16063l, 16067l, 16069l, 
16073l, 16087l, 16091l, 16097l, 16103l, 16111l, 16127l, 
16139l, 16141l, 16183l, 16187l, 16189l, 16193l, 16217l, 
16223l, 16229l, 16231l, 16249l, 16253l, 16267l, 16273l, 
16301l, 16319l, 16333l, 16339l, 16349l, 16361l, 16363l, 
16369l, 16381l, 16411l, 16417l, 16421l, 16427l, 16433l, 
16447l, 16451l, 16453l, 16477l, 16481l, 16487l, 16493l, 
16519l, 16529l, 16547l, 16553l, 16561l, 16567l, 16573l, 
16603l, 16607l, 16619l, 16631l, 16633l, 16649l, 16651l, 
16657l, 16661l, 16673l, 16691l, 16693l, 16699l, 16703l, 
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